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Bayesian Analysis Software User Manual

1. button and click the new button to create the directory To delete a WorkDir select the directory to be delete and activate the delete directory button Finally to load a WorkDir select the directory to be loaded and activate the load directory button 3 1 4 the Settings menu The settings menu is shown in Fig 3 7 This menu allows one to configure the interface to make use of the operating environment and to control the Markov chain Monte Carlo simulations Set the window size and to set so user preferences Here is a description of the this Settings menu the McMC Parameters submenu Many indeed most of the Bayesian Analysis packages use Markov chains to approximate the joint posterior probability for the parameters appearing in the model This is done by using the Markov chain to draw samples from the joint posterior probability for of the parameters From these samples Monte Carlo integration can be used to approximate the posterior probability for each parameter appearing in the model The number of Markov chain the number of samples gathered and the annealing schedule are things that the user can control i e configure Activating the McMC parameters widget brings up the popup shown in Fig 3 8 This popup allows number of Markov chain Monte Carlo simulations that are to be run concurrently or in parallel to be set Concurrently if only a single processor is available and in parallel if multiple processors are available Additional
2. Get Job Reset bmrw200 Constant O 81 Ascii Data Viewer FID Data Viewer Image Viewer Prior Viewer Fid Model Viewer Plot Results Viewer Text Results Viewer File Viewer standard Print Copy Save SaveAs Enable Editing scroll Up W Settings Instructions Probability model MCMC values Bayes params Console log Bayes accepted Image Abscissa Bayes Condensed Fortran Ist Probability model Bayes params Console log Log Output Model Status Summary Best Model Summary2 Best Summary Summary3 Best Regions Regions Parameter File Listing for the BayesExpGiven Package Created 02 Nov 2011 14 39 10 Output Dir Number Of Abscissa Number Of Columns Number Of Sets File Name File Name McMC Simulations McMC Repeats Total Mcmc Samples Total McKill Count Minimum Annealing Steps Histogram Type Outlier Detection Number Of Priors Low 0 0000E 00 1 0000E 06 Param Name Rate Amplitude 0 0000E 00 0 0000E 00 Given Exponential package by larry BayesOtherAnalysis I 1 2 BayesOtherAnalysis 001 dat BayesOtherAnalysis 002 dat 48 30 4 30 Binned Disabled 2 Mean High std Dev 2 0000E 00 1 0000E 06 Package Parameters Number of Exp 6 6667E 01 3 0000E 05 3 7417E 00 Gaussian 3 6262E 00 Gaussian Norm Prior Ordered LowHigh Notorder amp EXE Jue Figure 3 28 After a packa
3. 0 0 0 0EO 2 62E1 DecayRate o J Ea es Figure 3 18 The Prior Viewer is used on most packages and it allows one to view and modify the prior probabilities used in the calculation Here the viewer is displaying a prior we call a positive prior The positive prior has a number of very useful characteristics for scale parameters It goes to zero at zero thus preventing scale parameters from going negative It is asymptotically Jeffreys so allows the upper bound to be very large and it has a peak at a user specified location 64 THE CLIENT INTERFACE The prior selection box allows the user to select one of five different prior probabilities for a parameter Ounce selected the user can then specify the various elements that determine the prior shape In all cases the user must supply a prior range i e low and high parameter value However each prior type can have other characteristics that must be supplied by the user for example a Gaussian requires a mean and standard deviation Here is a description of the five priors and input requirements needed to generate a normalized prior Uniform selects a uniform prior probability having the user specified low and high parameter range Uniform prior probabilities are not typically used for continuous parameters although the user can certainly use them Rather the interface typically uses a uniform prior probability for expressing an interference between model
4. in Maximum Entropy and Bayesian Methods G R Heidbreder ed pp 1 42 Kluwer Academic Publishers Printed in the Netherlands 415 416 12 13 14 15 16 17 18 19 20 21 22 23 no i BIBLIOGRAPHY Bretthorst G Larry 1999 The Near Irrelevance of Sampling Frequency Distributions in Maximum Entropy and Bayesian Methods W von der Linden et al eds pp 21 46 Kluwer Academic Publishers the Netherlands Bretthorst G Larry 2001 Nonuniform Sampling Bandwidth and Aliasing in Maximum Entropy and Bayesian Methods in Science and Engineering Joshua Rychert Gary Erickson and C Ray Smith eds pp 1 28 American Institute of Physics USA Bretthorst G Larry Christopher D Kroenke and Jeffrey J Neil 2004 Characterizing Water Diffusion In Fixed Baboon Brain in Bayesian Inference And Maximum Entropy Methods In Science And Engineering Rainer Fischer Roland Preuss and Udo von Toussaint eds AIP conference Proceedings 735 pp 3 15 Bretthorst G Larry William C Hutton Joel R Garbow Joseph J H Ackerman 2005 Exponential parameter estimation in NMR using Bayesian probability theory Concepts in Magnetic Resonance 27A Issue 2 pp 55 63 Bretthorst G Larry William C Hutton Joel R Garbow Joseph J H Ackerman 2005 Ex ponential model selection in NMR using Bayesian probability theory Concepts in Magnetic Resonance 27A Issue 2 pp
5. 8 2 Bayes Analyze Models ou a oy ce oat alan aaa oo E d SES s 8 3 Bayes Analyze Short Descriptions aoa ews oec soa oem a a aa a e e e a 13 Chapter 3 the Client Interface The interface to the Bayesian Analysis software is a Java interface that runs on any machine having Java 6 or higher Assuming the Bayesian Analysis software has been installed on a server at your site for arguments sake lets call this machine your server net then the client interface can be displayed by issuing javaws http your server net 8080 Bayes launch jnlp where javaws is the Java web start utility and comes with most Java installations your server net should be replaced by the server name or IP address and 8080 should be replaced by the port number used during installation see Chapter 2 for a description of how to install the software When the interface starts it will displays the default start up page shown in Fig 3 1 This figure is a repeat of the figure shown in Chapter 3 Fig 1 1 and is repeated here for convenience The purpose of the start up page is to allow an analysis to be restarted When the interface exits or changes working directories the interface saves the current settings in a special Java properties file When the interface start it consults this file to determines what the last WorkDir was and how to restart that analysis If an analysis was saved the interface displays the messages shown in Fig 3 1
6. DecayRate From Max Prob Sim 0 99599 Data and Model Set 1 Residuals Only Set 1 Ex DecayRate vs Prob Decay Decimo vs Prob m Mant Ge Dvs Prop Mzinfty Get 1 Mzinfty Set 1 vs Prob Rms Set 1 Apr Seis Prob Nose Standard Deviation Get Noise Standard Deviation Get Log Lkellh Log Prcbability Probability Density L Get Maxere Histooram 0 375 0 980 0 985 0 990 0 995 1 000 1 005 1 010 1 015 1 020 View Samples J DecayRate O tS Figure 3 22 The whole purpose of the Markov chain Monte Carlo simulation is to derive an ap proximation of the Bayesian posterior probability for the parameters appearing in a model To do this a Markov chains is used to gathers samples from the joint posterior probability for all of the parameters and then uses Monte Carlo integration to obtain samples from the posterior probabili ties for the individual parameters These samples are then smoothed binned and displayed in plot like the one shown here This particular plot is for the posterior probability for the smallest decay rate constant in a biexponential model containing a constant probability If multiple data sets were processed then the output plot list area will contain multiples of these data model and residual plots one set for each data set 3 4 6 2 the Posterior Probabilities Plots All of the Bayesian analysis packages with two exceptions use Markov chain Mon
7. Image Abscissa will display the file BayesHome WorkDir images Abscissa if its available This file is used in image processing to tell the Ascii model files what the abscissa values are for the Ascii model Consult the Section A for more about this file Bayes Condensed displays the file BayesHome WorkDir BayesOtherAnalysis Bayes Condensed File an example of this file is shown in Fig 3 29 The file consists of one line per parameter in the model Each line contains the parameter name the mean and standard deviation of the parameter computed from the simulations and the parameter value taken from the simulation that had maximum posterior probability The header shown in this figure is not present in the actual condensed file that header was put in the figure only as an aid in identifying the various fields The names shown in this plot are generally the names assigned to the parameter by the user or by us when we wrote the code These names should be simple and self explanatory As illustrated in Fig 3 29 the interface will modify the names of the amplitudes and noise standard deviations by appending a data set number to them when multiple data sets are used In this example the data set numbers are the 01 and 02 suffixes So for example BayesExpGiven Amplitude_2 02 is the amplitude assigned to decay rate 2 in data set number 02 Similarly BayesExpGiven Amplitude_2 01 is the amplitude number 2 in data set 01
8. 421 reprinted in Maximum Entropy and Bayesian Methods in Science and Engineering 1 pp 1 24 G J Erickson and C R Smith Eds 1988 Jaynes E T 2003 Probability Theory The Logic of Science edited by G Larry Bret thorst Cambridge University Press Cambridge UK Jeffreys Harold Sir 1939 Theory of Probability Oxford Univ Press London Later editions 1948 1961 Jones John G 2001 Michael A Solomon Suzanne M Cole A Dean Sherry Craig R Malloy An integrated 7H and C NMR study of gluconeogenesis and TCA cycle flux in humans American Journal of Physiology Endocrinology and Metabolism 281 pp H848 H856 Kotyk John N G Hoffman W C Hutton G Larry Bretthorst and J J H Ackerman 1992 Comparison of Fourier and Bayesian Analysis of NMR Signals I Well Separated Resonances The Single Frequency Case J Magn Reson 98 pp 483 500 Laplace Pierre Simon 1814 A Philosophical Essay on Probabilities John Wiley amp Sons London Chapman amp Hall Limited 1902 Translated from the 6th edition by F W Truscott and F L Emory Lartillot N and H Philippe 2006 Computing Bayes Factors Using Thermodynamic Inte gration Systematic Biology 55 2 pp 195 207 Le Bihan D 1985 E Breton Imagerie de diffusion in vivo par rsonance C R Acad Sci Paris 301 15 pp 1109 1112 Lomb N R 1976 Least Squares Frequency Analysis of Unevenly Space
9. 64 72 Bretthorst G Larry William C Hutton Joel R Garbow Joseph J H Ackerman 2005 How accurately can parameters from exponential models be estimated A Bayesian view Concepts in Magnetic Resonance 27A Issue 2 pp 73 83 Bretthorst G Larry W C Hutton J R Garbow J J H Ackerman 2008 High Dynamic Range MRS Time Domain Signal Analysis Magn Reson in Med 62 pp 1026 1035 Chandramouli Visvanathan Karin Ekberg William C Schumann Satish C Kalhan John Wahren and Bernard R Landau 1997 Quantifying gluconeogenesis during fasting Amer ican Journal of Physiology 273 pp H1209 H1215 Cox R T 1961 The Algebra of Probable Inference Johns Hopkins Univ Press Baltimore d Avignon Andr G Larry Bretthorst Marlyn Emerson Holtzer and Alfred Holtzer 1998 Site Specific Thermodynamics and Kinetics of a Coiled Coil Transiton by Spin Inversion Trans fer NMR Biophysical Journal 74 pp 3190 3197 d Avignon Andr G Larry Bretthorst Marlyn Emerson Holtzer and Alfred Holtzer 1999 Thermodynamics and Kinetics of a Folded Folded Transition at Valine 9 of a GCN4 Like Leucine Zipper Biophysical Journal 76 pp 2752 2759 Gilks W R S Richardson and D J Spiegelhalter 1996 Markov Chain Monte Carlo in Practice Chapman amp Hall London Goggans Paul M and Ying Chi 2004 Using Thermodynamic Integration to Calculate the Posterior Probability
10. Frequency Estimation o lt o o oca aap cewa g kaaa a E E EE e a 123 Estimating The Sinusoids Parameters o e oo oor birra daa 125 the Exponential interface 202 acm exe eee a REESE ER Pees 130 the Unknown Exponential interface 0 0020000 ee eee 136 Tbe Distribution of Models 2 21 4 2424240608480 44b444 ene 141 Exponential Probability for the Model o a 142 the Inversion Recovery interface e e e e 144 Bayes Analyze Interface escasa Aaa 148 Bayes Analyze Fid Model Viewer een 152 The Bayes Analyze File Header ee 170 The bayes mbise Wiles oe ee o eH REA eee ee ee 172 Bayes Analyze Global Parameters 2 een 175 Bayes Analyze Model File 2 2 ee 176 Bayes Analyze Initial Model ee 178 Base qD Locarthm Or her QUOS wo aaa a aed ee A Oe A A an 178 The bayes outp t nbnnn Report 2 222222 93 he eS 179 Bayes Analyze Uncorrelated Output ee ee 180 The bayes probabilitiesmnnn File oo se e sass circos 182 The bayeslos n nn Pie 25 a See ke sop p AS a aaa a 185 The bayes status onon File ccoo odie rss EEE SS 187 The b ayes modelonan Fil 2222 99 cs a ERE RE OR Pes 188 The bayes model nnnn File Uncorrelated Resonances rss 189 Bayes Analyze Summary Header e 189 The Summary2 Report 2444 2 264 Rx m ee don ae RSCECRSCECY ek m 190 The Summary2 Report s s cls sma 9 d
11. Own ASCII Model 22 Ascii Model Selection 23 Phasing An Image 23 1 The Bayesian Calculation visera d Re eee ee ea be a 23 2 Using The Package 267 269 273 277 279 279 280 282 285 287 288 289 291 295 297 300 303 303 306 307 309 310 311 312 313 314 321 323 323 324 327 329 331 24 Phasing An Image Using Non Linear Phases 241 The Model Eguation ss 2 24321 x A 24 2 The Bayesian Calculations 22s m RR 24 9 The VnmrJ and Vamo Interfaces 2 222226 RA 28 Analyze Image Pixel 28 1 Modification History uu 264 4 44 800 om SUE dee oo de A 29 Image Pixel Model Selection A Ascii Data File Formats A Ascii Input Data Files os o icicu a a S RR RR A A 2 Ascii Image File Formats llle A 3 The Abscissa File Format e irs ae eceu aca eee e 00000 B Markov chain Monte Carlo With Simulated Annealing B 1 Metropolis Hastings Algorithm o llle B 2 Moaltiple Simulations cn ee ee a Bo eaumulated Annealine oo cs 2619 9c r a B 4 The Annealing Schedule lt lt o eee Bb Killine Simulations a menm 9o UE G44 GRE SS B6 the Proposal s soca kk wees ee ee eA a Cee ds C Thermodynamic Integration D McMC Values Report E Writing Fortran C Models E 1 Model Subroutines No Marginalization E 2 The Parameter File 2 22 22 204660404 b44h 4044 E 3 The Subroutine Interface o e leen E 4 The Subroutine Declarations lt 2 e0e0
12. The Fid Data Viewer the Options Menu a 54 The Image Viewer 2c won x Sog x xe heme OX OE emm OE PEOR ERR cR dU EOS 57 The Image Viewer Right Mouse Menu o e eee 58 he Prior Viewer I ie eae OEGE O e c9 wd 3 box ERS ss 63 The Fid Model Viewer 2 2 o 242 ses RR Es ERE Ge ee EEE SS 66 The Data Model and Residuals ociosa GSE m9 e m aaa ee es 69 The Plot Information popup cc soa 44 5 Ae a memor om ek ee Re 70 The Posterior Probabilities aos s so areca tie oo 71 The Posterior Probabilities Vs Parameter Value noana o 73 The Posterior Probabilities Vs Parameter Value a Skewed Example 74 The Expected Log Likelihood o o e eee ee eee 76 The Seatter PloUS 22x33 ope oum a vom SDE ald 77 The Los Probability Plot 4 oO Wo SS sie eee Ga OY ORR Ged 79 The Text Results Viewer cocinera 644 04 2 oe eee ee eee bees 81 The Bayes Condensed File Room m mme A 84 Bortran C Model VIeWeE osse en ex E PIONEER Ey Ye es 87 Portia C Model Viewer vs oss aes RE 3 eo A es 88 10 4 1 4 2 4 3 4 4 4 5 4 6 4 7 5 1 6 1 6 2 6 3 Fe 8 15 8 16 8 17 8 18 Oo 9 2 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 Frequency Estimation Using The DFT o o 104 JAMASeS TAR 105 Nonuniformly Nonsimultaneously Sampled Sinusoid sss 119 AMAS SPACE e RD c 120 Which ls The Critical Time o sa iie s iio ee 09 3 Ge 9 ed ea eS 122 Example
13. WorkDir No attempt is made to change the name of an image so loading images with the same name will result in replacing the old image We will briefly mention the various types of data that can be loaded and give a brief description of the file formats Varian k space fid will bring up a popup that allows navigation loading of standard Varian k space image fid The selected file must be suffixed with fid and a Varian binary file is expected The binary is copied into the image fid Subdirectory in the current WorkDir It is then Fourier transformed phased and three img file are written into the images Subdirectory These three files are named LoadedImage Abs 4dfp img LoadedImage Real 4dfp img and LoadedImage Imag 4dfp img and contain the ab solute value imaginary and real images Text k space fid will bring up a popup that allows navigating to and load a text k space image fid The selected file must be suffixed with fid and a Varian binary file is expected The binary is copied into the image fid Subdirectory in the current WorkDir THE CLIENT INTERFACE 33 Varian k space fid loads a Varian k space fid Wa ri ati k 5 p ace FI D and converts it to a 4dfp stack Text k space fid loads an ASCII Text k space Te xt k p ace Fl D fid and converts it to a 4dfp stack FDF loads and FDF stack of images and reorders FD F and converts it to a 4dfp stack F Binary 4dfp img loads 4dfp stack of
14. are not in equilibrium However when one reaches the sample gathering phase the simulations are should be in equilibrium Here equilibrium means that as the Markov chain Monte Carlo simulations are run the details of each simulation change but the expected values of the parameters probabilities likelihoods etc remain constant i e the system is at a static equilibrium In the literature this condition is often called detailed balance In the sample gathering phase the simulations are run through a predetermined number of steps and then each simulation is save This process is repeated until all of the user specified repeats have been gathered Each line in the plot shown in Fig 3 27 is the logarithm of the posterior probability for one of the simulations as a function of repeat number As the simulations are run the posterior probability for a given simulation is increasing and decreasing as a function of the repeat number When all of the simulations are doing this the simulations are often said to be mixing Indeed in this plot the simulations are mixing so well that it is impossible to follow the trajectory of a single simulation However note there is a fairly sharp maximum that bounds the posterior probability This bound reflects the fact that the model can only fit the data so well Individual simulations come up to the maximum and then move away from it Here the size of the deviations from this maximum are on the order of a few e fold
15. bility Because the data are not being used the fit to the data is very bad and consequently the expected logarithm of the likelihood starts out at a very low number As the annealing parameter is increased the logarithm of the likelihood contributes more and more to the calculation and so the expected logarithm of the likelihood increases coming to a maximum when the model has fit the data as well as possible All the packages that run Markov chain Monte Carlo simulations run multiple simulations in parallel The expected logarithm of the likelihood shown in Fig 3 25 is the average of logarithm of the likelihood over all of these simulations See Subsection B for a more detailed discussion of simulated annealing and Markov chain Monte Carlo 3 4 7 2 the Scatter Plots There are two additional plot types that need to be discussed scatter plots and the logarithm of the posterior probability plot Scatter plots are generally toward the bottom of the output plot list and have have names of the form parameter 1 vs parameter 2 where parameter 1 amp 2 are any two parameters from the simulations An example scatter plot is shown in Fig 3 26 This particular example was generated using the exponential package with a biexponential model plus a constant Many samples are drawn from the joint posterior probability for the parameters In the example shown here there were 50 simulations and 30 samples were drawn from each simulation so there are a total
16. directory for each sample ran the model selection and then save the resulting working directories At a latter time it was necessary to reload all 100 working directories so that we could review and in some cases rerun the analysis 3 1 2 the Packages menu The packages menu shown in Fig 3 4 is used to select a package a set of programs used to solve some particular problem The software contains roughly 20 packages and these packages implement various calculations using Bayesian probability theory The various packages implemented by this software are briefly describe here and a detail description of each package is given in later Chapters Exponential The Exponential package estimates the decay rate constants and amplitudes of signals known to be decaying exponentially It does this when the number of the exponentials is known or unknown In both cases the input to this package can come from ASCII files from a peak pick or from Bayes Analyze files In all cases one or more input data sets can be processed When multiple input data sets are processed the package looks for exponentially decaying signals that are common to the various data sets but allowing each exponential to have differing initial conditions in each data set See Chapter 5 for more on the exponential problem when the model is given and Chapter 6 when the number of exponentials or the present of a constant offset are unknown Inversion Recovery The Inversion Recovery package
17. file and allows one to view the Ascii file as text In the plotting area a right mouse click brings up a submenu that allows one to configure the plot For example a right mouse click to can be used to change the headings axis labels and to save or print the plot On the left hand side at the bottom there are two widgets one labeled Delete and one labeled that delete the selected file or show information about the selected file These functions are redundant with the functions available using a right mouse click Finally on the plotted area a left mouse click and dragging the cursor down and to the right will select highlight a region When the cursor is released the highlighted are is expanded To return to the full plot left mouse click and drag the cursor up and to the left will restore the plot Gm 2 3 4 2 the fid Data Viewer The Fid Data Viewer shown in Fig 3 13 is activated whenever fid data is loaded from the Files menu or when the Fid Data Viewer is selected This viewer allows one to look at both the time and frequency domain fid data When an fid is loaded the fid is copied into the fid directory in the current WorkDir and written in Varian format The data is then Fourier transformed the Fid Data Viewer is activated the spectral data is phased and plotted Additionally like the afh file an ffh file is written that contains information about the fid This f h file is displayed whenever informa
18. for which the posterior probability was maximum in the example shown this value is 0 99599 For plots like the one shown the peak in the histogram and the parameter that maximized the posterior probability are essentially the same However it is possible for the parameter value at the peak of the histogram and the parameters from the simulation having maximum posterior probability to be very different For example in Fig 3 24 the resulting histogram and the samples have been plotted on the same scale The histogram is shown as the line in this plot and the samples are the open circles In this example the peak of the histogram is about 0 1 while the sample that had maximum posterior THE CLIENT INTERFACE 73 Package Bayesian Build Your Own 1D Model WorkDir AbscissaTesting Host radest02bmr702 rad wustl edu File Package WorkDir Settings Utilities Help InvRec f Priors have been saved Submit Job to Server Server Load and Build Model Analysis Options Save Reset RUN j Cancel ser Staus system User Find Outliers Save Get Job Run radest02bmr702 Build Save priors Reset Ascii Data Viewer HD Data Viewer Image Viewer Prior Viewer Fid Model Viewer lot Resuts Viewer Text Resuts Viewer File Viewer Fonran C Model Viewer Output Plots Scatter Plot Of The DecayRate vs Posterior Probability Mean 0 99611 Sd 6 54E 03 DecayRate From Max Prob Sim 0 99599 Data Model and Resia Set
19. images E Ina ny a dip A Ii q General Binary brings up a popup that will at tempt to load a general binary file G ene ral E Mad ry Bruker single 2dseq brings up a popup loads a single Bruker 2dseq file E ru k er Sin gl 2 Se a Bruker 2dseq Stack brings up a popup loads a i Bruker stacked 2dseq file B ru k er 2 d Sg q Sta ck Single Column Text File brings up a popup Loads single column text images Single Column Te xt File Multi Column Text File brings up a popup Loads multi column text images M LI Iti xy Col um Te xt Fi Siemens IMA brings up a popup Loads Siemens IMA images Siem ens IMA DICOM brings up a popup Loads DICOM im DICOM o Figure 3 3 When the Files Load Image selection menu is selected this pull down menu is displayed It is used to select the type of image data to be loaded After selecting a data type a popup will be displayed that will allow navigation to the appropriate loading of the data In most cases the popup will have a number of configuration parameters that have to enter 34 THE CLIENT INTERFACE It is then Fourier transformed phased and a three img file are written into the images Subdirectory The image files images are names as discussed in the previous item FDF will bring up a popup that allows navigating and loading of Varian FDF images One or more of the FDF files are loaded by the open button This will copy and reformat the FDF images into a single 4dfp file located in
20. images into a single 4dfp file located in the THE CLIENT INTERFACE 35 images Subdirectory of the current WorkDir The interface attempts to order the images internally so that the displayed images are in the proper slice and array order Load Abscissa is submenus on the Files menu When selected it brings up a popup that allows the user to navigate to an to a file and then load it as an Abscissa file Abscissa files are stored in the images Subdirectory and are named Abscissa Abscissa files can be multicolumn ASCII files The abscissa is used for several purposes for example it is used to generate ASCII files from image pixel data Additionally when an image is processed on a pixel by pixel basis the model that does the processing must know the abscissa values For example if one is processing diffusion tensor data one must know the B values The B values are the abscissa and in this example the abscissa file would be a three column ASCII file The number of columns in the selected Abscissa file must match the requirements of the current package before the interface will load the file When the Load Abscissa button is activated one can select one of two options From File will bring up a popup that allows navigating to and loading of an Abscissa file From Procpar will bring up a popup that allows navigating to and selecting a procpar file The interface will then read the procpar and find the arrayed variable
21. imum pixel values When this button is activated it will popup a widget in which a minimum and maximum pixel values can be entered After entering these values selecting OK will cause the statistics to be calculated and updated These updated statistics will ignore all pixels below the minimum or above the maximum If no ROI is present then the statistics are generated for the entire image Save Statistics will bring up a popup that allows navigation and saving of the statistics Here is an example of the saved statistics Min 9 0002e 00 Mean 9 4447e 00 Max 9 9981e 00 SDev 2 8362e 01 RMS 2 8362e 01 Pixels 1292 62 THE CLIENT INTERFACE and this output is left justified in the saved file Note all statistics generated are for a single image there are no capabilities in the interface for applying the statistics calculations across multiple images 3 4 4 Prior Viewer The Prior Viewer is used by almost every package and as its name implies it is used to view modify and generally set up the prior probabilities used in the Bayesian calculations The viewer is shown in Fig 3 18 In its appearance and function it is very similar to the Ascii Data Viewer Fig 3 12 Along the left hand side is a list of priors that can be modified and on the right is a plotting area where the priors are plotted In the example shown it is the prior probabilities for the an inversion recovery model that are shown Inversion recover models are si
22. in Bayesian Model Selection Problems in Bayesian Inference and Mazi mum Entropy Methods in Science and Engineering 23rd International Workshop Volume 707 pp 59 66 BIBLIOGRAPHY 417 25 26 27 28 29 30 31 32 33 34 35 36 37 38 Holtzer Marlyn Emerson G Larry Bretthorst D Andr d Avignon Ruth Hogue Angelette Lisa Mints and Alfred Holtzer 2001 Temperature Dependence of the Folding and Unfolding Kinetics of the GCN4 Leucine Lipper via 13C alpha NMR Biophysical Journal 80 pp 939 951 Jaynes E T 1968 Prior Probabilities IEEE Transactions on Systems Science and Cyber netics SSC 4 pp 227 241 reprinted in 29 Jaynes E T 1978 Where Do We Stand On Maximum Entropy in The Maximum Entropy Formalism R D Levine and M Tribus Eds pp 15 118 Cambridge MIT Press Reprinted in 29 Jaynes E T 1980 Marginalization and Prior Probabilities in Bayesian Analysis in Econometrics and Statistics A Zellner ed North Holland Publishing Company Amsterdam reprinted in 29 Jaynes E T 1983 Papers on Probability Statistics and Statistical Physics a reprint collection D Reidel Dordrecht the Netherlands second edition Kluwer Academic Publishers Dordrecht the Netherlands 1989 Jaynes E T 1957 How Does the Brain do Plausible Reasoning unpublished Stanford University Microwave Laboratory Report No
23. menu has many functions im Display Full Image ages to be delete the gray scale can be adjusted Delete Selected pixel information can be displayed Pixels can be Delete All viewed as text look at a histogram Finally the Autoset Grayscale For Entire Stack image stack can be exported to ImageJ This fea Autoset Grayscale For Current Image ture allows use all of the facilities in ImageJ to View Selected Pixels as Text Md eee E Load Selected Pixels Show Histogram Copy Selected Images As Copy All Images As Save Displayed Image As gt Export to Image Show info Image Viewer Settings Figure 3 17 When the Image Viewer is running a right mouse click brings up this menu This menu can be used to delete images load ROI pixels into the Ascii Data Viewer export an image stack to ImageJ and a number of other useful functions Show Histogram will load the pixel values as a histogram Copy Selected Image As will copy a selected image stack to a new name and location Copy All Images As will copy all image stacks to a new directory Save Displayed Image As will save the currently displayed image as a jpg png tif or bmp image Export to ImageJ will export and open the image to in ImageJ Show info will display everything know about an image Image Viewer Settings will bring up a popup that configures the Image Viewer 3 4 3 2 the Set Image area The bottom left area shown in Fig 3 16 is used to set the image that is currentl
24. of 1500 samples The scatter plot shown in Fig 3 26 is of Rate_1 vs Rate_2 Each point in this plot is one of the 1500 simulations The coordinates of each point are the values of the decay rate constants in a given simulation Scatter plots can look like an ellipsoid that is aligned with the axes in which case the parameters are uncorrelated Scatter plots can also be tilted like the one shown in Fig 3 26 in which case the parameters are correlated Finally scatter plots can take on highly irregular shapes and can even have sharp cutoffs when parameters have natural bounds The scatter plot shown in Fig 3 26 is an almost classical example of a scatter plot of two correlated parameters Note the almost linear like upward scatter in this plot This type of feature is indicative of a correlation between the sum and difference of the decay rate constants The density of points in a scatter plot is a sample from the 76 THE CLIENT INTERFACE Given and Unknown Nun f Exponentials Submit Job to Server Analysis Option SaveReset RUN Cancel Set Order 2 w Find Outliers O Get Job Run Include Constant Ascii Data Viewer FID Data Viewer Image Viewer Prior Viewer Fid Model Viewer Plot Results Viewer Text Results Viewer File Viewer Output Plots Expected Log Likelihood Data Model and Resid Set 1 N 340 Data and Model Set 1 345 Residuals Only Set 1 350 Rate_1 355 j
25. out the individual prior to be removed Derived widget is identical in its behavior as the Priors widget The derived label contains the current number of derived parameters and the grayed out down arrow on the right size allows you to add remove and remove derived parameters Compile On Server will send the current version of the model to the server to compile Note that this is a simple compile and it does not save the model in your BayesAsciiModels subdirectory Cancel And Exit will cancel you current modifications and the Create Enter Ascii model window will exit Note that if you had activated the Save and Load button those changes will still be in effect when cancel is activated Save and Load will save your current modifications and the reload the model so that when you exit the popup model editing window your changes are ready to be run Along the top of the popup Edit Create Ascii model are three additional widgets here is a description of their function Code will display the current code including any modifications you have made to the code The window displaying the code is a simple editor and you can make changes to the code as you see fit 90 THE CLIENT INTERFACE Parameters will display the current parameter file any modifications you have made to the pa rameters The window displaying the code is a simple editor and you can make changes to the code as you see fit The window displaying the parameters is not quit
26. s s 605s e ea boo a ee ee hee Oe ed eS 10 3 1 The IPGD D20 Metabolite 22222 kk RRR RR RRA A RE Rm 10 3 2 The Glutamate 2 0 Metabolite ra 6 2066 62244408 28 ee eee es 10 3 3 The Glutamate 3 0 Metabolite 10 4 The Example Metabolite o llle 10 5 Outputs From The Bayes Metabolite Package o o llle 11 Find Resonances 11 1 The Bayesian Calculations 21e RR REX A 11 2 Outputs From The Bayes Find Resonances Package o o 12 Diffusion Tensor Analysis 12 1 The Bayesian Calculation nic RO moo e de A oe ee eS 12 2 Using The Package 13 Big Magnetization Transfer 13 1 The Bayesian Calculation sics x09 x a 4 x XO memo RR R ROR aS 13 2 Outputs From The Big Magnetization Transfer Package 14 Magnetization Transfer 14 1 The Bayesian Calculation y isis ede 33e he ee De ee ee we ee 14 2 Using The Package 167 169 169 174 175 177 181 184 187 188 189 190 191 192 197 199 206 209 213 215 218 218 222 225 226 228 229 231 236 237 244 15 Magnetization Transfer Kinetics 151 The Bayesian Calculation amp 2442044448 044 ooo poe mo 9 Rok RR eee eee y 3 15 2 Using The Package 16 Given Polynomial Order 16 1 Theo Bayesian Calculatiu uuu wa mme eR oh cy ORG GE A DR a S TO Ll Gram Schmidt g coa dor aa RR ede ei S ooh eR Rum m moe e ge dd du 16 1 2 Th Bayesian Calculation oca 24 roa sco ck m kon tmr RR RUE RR n RO AU 1
27. the images Subdirectory of the current WorkDir The input images are ordered so that the displayed images are in the proper slice and array order Binary 4dfp img will bring up a popup that allows navigating and loading of 4dfp file The 4dfp file is copied into the images Subdirectory The 4dfp file type is the internal standard in which all images are stored in the Bayesian Analysis software so no additional processing is needed See Appendix G for a description of 4dfp files General Binary Bruker single 2dseq Bruker 2dseq Stack Single Column Text File will bring up a popup that allows one to navigate to a single column text file and load it into the images Subdirectory The single column text is read by the interface and then parsed into images with the assistance of a popup window The popup will display the total number lines in the text file and the row column slice and array dimensions must be set so that the total pixels is equal to the total lines Until these dimensions are set correctly the interface will not load the image Multiple images can be stacked in the file If so they can be stacked either in slice or array order and specify which order is used when the data are loaded The default outer loop the most slowly varying loop is the array dimension with slice as the inner loop Multi Column Text File will bring up a popup that allows navigating and loading of a Multi Column text file Multi Column text files imag
28. the currently loaded Models This list is a selection menu and by left mouse clicking on a model the model will be displayed by the Fortran C Model Viewer If multiple models are loaded then clicking on each model displays that model Remove Selected Model will delete the model from you Bayes Home BayesAsciiModels Subdi rectory Note that when system models are loaded they are copied to the BayesAsciiModels Subdirectory and removing them will remove them from the Subdirectory it will not remove them from your system directory Edit Create New Model will open the current model in an editor and allow you to make changes to the model The modified model can be saved using the current name or it can be renamed For a description of how to write Fortran C models see Section E Code will display the source code of the currently selected model Note in this viewer neither the model nor the parameters is editable However the priors can be changed on the Prior Viewer THE CLIENT INTERFACE 87 Package Bayesian Build Your Own D Model a WorkDiratestu sHostabayes File Package WorkDir Settings Utilities Help Example_NoMarg f Not Built Submit Job to Server Server Load and Build Model Analysis Options Run j Cancel Set Status system user FindOutiers Get Job Not Run bayes Build Save priors Ascii Data Viewer FID Data Viewer Image Viewer Prior Viewer Fid Model Viewer Plot Results Viewer Text Results Vi
29. the interface will dynamically generate a time domain fid Model and then Fourier transform phase and display the model in this viewer This viewer is very similar to the Fid Data Viewer discussed in Section 3 13 Indeed the under lying Java class that defines this viewer is the same as the Fid Data Viewer here it has had a few additional functions added to it In Section 3 13 we discussed the widgets along the bottom of the viewer and three of the widgets on the top part of the viewer the Trace spinner the Data Type selection and the Options widgets The functions of these widgets is identical to their function on the Fid Data Viewer and consequently we refer the reader to Section 3 13 for those discussions There are three main differences from fid Data Viewer first the presence of the pull down menu containing the word Trace This widget allows different types of displays to be selected and we will give a description of the displays shortly Second is the presence of the Build BA Model For fid button This button allows one to build and view a model fid and again we will have more to say about this shortly Finally the entry box just to the right of this button specifies the trace that is to be modeled 3 4 5 1 The fid Model Format Some packages generate fid models when they run Big Peak Little Peak and the Metabolite package both do this and some packages Bayes Analyze and Find Resonances generate Ascii Mod
30. the lines starting To restore analysis This line contains the name of the package that was being processed in this case the package name was AnalyzelmagePixels and the analysis was saved in a WorkDir named Given If the Restore Analysis button is activated then the Given AnalyzeImagePixels analysis will be restored to its previous status When the interface finishes restoring the analysis it will function exactly like WorkDir or interface was never exited If an analysis is not to be restored then changing the package will delete the contents of the current WorkDir and configure the WorkDir for the new package If another analysis is running in a different WorkDir then changing the current working directory using the WorkDir menu will cause the interface to switch to the new WorkDir and the previous analysis will be restored Finally if a completely new WorkDir is needed then selecting WorkDir Edit will bring up a popup that can create a new WorkDir After the WorkDir is create the first thing that must be done is to select a package 29 30 THE CLIENT INTERFACE Bayesian Analysis of Common NMR Problems version 4 01 File Package WorkDir Settings Utilities Help To start new analysis select the package you wish to run under Package menu 3 Washington University in St Louis To restore analysis BayesEnterAscii saved in AbscissaTesting press Restore Analysis SCHOOL OF MEDICINE button
31. this prior goes to zero at zero and is asymptotically Jeffreys the prior must have a peak value This peak is also seen in Fig 3 18 and as it turns out the prior is essentially characterized by the location of this peak The functional form of the prior is given by 1 X z if Low lt X lt High P X Peak Norm X Peak 3 7 0 otherwise where X is the parameter Low is the low parameter range usually zero in this prior High is the largest parameter value and Peak is the location of the peak In the numerical calculations Norm is set using the procedures described above Parameter is a prior used in the Bayesian Software package when a parameter is to be set to a constant This prior is essentially a delta function and allows no variation in a parameter As a computational note the Markov chain Monte Carlo simulations do not vary any parameter that has a prior type set to parameter There are a few packages that make use of this prior For example the enter Ascii Model package makes use of it as a means of passing THE CLIENT INTERFACE 65 the calculation routines parameters For example a diffusion tensor model typically needs a conversion constant computed from some spectrometer settings These spectrometer settings are passed to these modes as parameters and the models use them to compute the conversion factors As explained above when these priors are used they are discretized and normalized to ensure that they s
32. while the displayed fid is not initially zoomed before phasing it can zoom as needed When the phased has been set hitting the Phase fid button will set the phase on all traces in the data The popup contains a Trace button that allows the displayed trace to be changed and it allows the type of data shown to be changed So for example one could phase the imaginary part of the spectrum if desired Finally the popup also allows the phase to be Reset to the loaded values Set Regions Brings up a popup that displays the currently set regions Regions low to high frequency intervals are used in the Bayes Analyze Regions report to calculate the total intensity in a given set of regions To use this popup simply set a low high region using the left and right cursors When a region is set hit the Mark button to add the region to the regions file Note the Delete button can be used to remove a region and the Close button will save the regions file The regions file is save in the current WorkDir in the BayesAnalyzeFiles Subdirectory This newly created regions file will be used in the regions report the next time Bayes Analyze package is run Set Fn is a pull down menu that allows the size of the Fourier transform to be set The pull down menu contains powers of two from 1K up to 256K that can be used in the calculations Set Reference brings up a popup that allows the current reference frequency to be set At the bottom of t
33. 1 j Data and Model Set 1 Residuals Only Set 1 950350 DecaMtate 0 0525 DecayTime 020598 Decayrime ys Pron 0 0475 Nalnit Set y a Wzinit Get 1 vs Prob M aad Wainfty Get D 0 0425 Nzinfey Got 1 vs Prob mpRms Set AmpRmns Set 1 vs Prob Noise Standard Deviation Set Noise Standard Deviation Set Lon Likelihood gt Log Probability 0 0400 0 0375 0 0350 0 0325 0 0300 0 0275 0 0250 0 0225 0 0200 0 0175 UnNormalized Posterior Probability 0 0150 0 0125 9 0100 0 0075 0 0050 E 0 0025 Get MaxEnt Histogram ow La 0 0000 lew samples 0 975 0 380 0 985 0 990 0 335 1 000 1 005 1 010 1 015 1 020 DecayRate Figure 3 23 In addition to plotting the posterior probability for the parameter the unnormalized posterior probability for the parameter is plotted against the parameter value used in evaluating the posterior probability As illustrated here for well peaked posterior probabilities these samples will look almost exactly like the binned histogram Fig 3 22 74 THE CLIENT INTERFACE 0 06 0 05 0 04 0 03 0 02 0 01 0 0 088 0 092 0 096 0 10 0 104 0 108 0 112 Figure 3 24 When the peak of the posterior probability is not symmetric or only weakly a function of a given parameter then it is possible for the parameters of the simulation that had maximum posterior probability to be significantly different from the mean of the Markov chain
34. 39E 00 BayesExpGiven Amplitude_2 02 9 70180E 00 1 69333E 01 9 52261E 00 BayesExpGiven AmpRms Set 2 1 39556E 01 2 46988E 01 1 36957E 01 BayesExpGiven NoiseStdDev 02 1 07327E 00 5 41963E 04 1 07274E 00 BayesExpGiven RmsAmplitude_1 7 22218E 01 1 31372E 00 7 08533E 01 BayesExpGiven RmsAmplitude_2 7 19484E 01 1 22696E 00 7 06506E 01 BayesExpGiven RmsAmpTotal 1 01944E 02 1 79284E 00 1 00058E 02 Figure 3 29 The Bayes Condensed File is shown here This file is a condensed version of the outputs found in the Mcmc Values report The file consists of one output line for each output parameter including derived parameters Each output line consists of the parameter name the mean value computed and standard deviation of the samples gathered in the Markov chain Monte Carlo simulation The peak parameter value is the value of the parameter in the simulation that had peak posterior probability The heading line shown in this Figure is not present in the condensed file it is here only to aid in describing the parameters THE CLIENT INTERFACE 85 probability model is a file containing the probability for the model Its function is similar to that displayed in the Standard output but the the way the file is produced and the format of the file are completely different In the Bayes Analyze outputs the Probability model file contains one line for each resonance added to the model These lines contain a description of the model the logarithm of the posterior probability
35. 6 2 Outputs From the Given Polynomial Order Package 17 Unknown Polynomial Order Inl Bayesian Calculations lt e 20 26422 wae ee eee beet ech Ho y eid 171 1 Assigning Priors oe ak a Rand 36308 03 Rae he EDAD REC acs 17 1 2 Assigning The Joint Posterior Probability l l 17 2 Outputs From the Unknown Polynomial Order Package 18 Errors In Variables 18 1 The Bayesian Calculation oa su ac 9 ws E Dew es 18 2 Outputs From The Errors In Variables Package 08 19 Behrens Fisher 19 3 Bayesian Caleilabiol lt sepais Lom eo O A DA RR ee ds 19 1 1 The Four Model Selection Probabilities 19 1 1 1 The Means And Variances Are The Same 19 1 1 2 The Mean Are The Same And The Variances Differ 19 1 1 3 The Means Differ And The Variances Are The Same 19 1 1 4 The Means And Variances Differ 19 1 2 The Derived Probabilities 2212 3333 kb 9 o8 o wo A wR ta 19 1 3 Parameter Estimation esos sassa 644444 ses e5GG 45 eee eda s 19 2 Outputs From Behrens Fisher Package eee eee eee 20 Enter Ascii Model 20 1 The Bayesian GCalcilatione 2421 ee ae Se eee AAA RR eS 20 1 1 The Bayesian Calculations Using Eq 20 1 o oo 20 1 2 The Bayesian Calculations Using Eq 20 2 o oo 20 2 Outputs Form The Enter Ascii Model Package 21 Test Your
36. 8 2 The Bayes Analyze Model Equation 2 e 153 8 3 The Bayesian Calculations cea see we are Y EG 8 ONS a 159 8 4 Levenberg Marquardt And Newton Raphson s 163 8 5 Outputs From The Bayes Analyze Package o o e 8 5 1 The bayes params nnnn and bayes model nnnn Files 8 5 1 1 The Bayes Analyze File Header o 85 1 2 The Global Parameters 0 723 o ri 8 5 1 3 The Model Components aa occu u e e e a 802 The bayesoubput nbne Piles 2 4 42 66844 aa a A a ee 8 5 3 The bayes probabilitiesnnnn File ca es o toai aaeeea du rua 8 5 4 The bayes log nnnn File lt a d ehia aa a a a ee ee 8 5 5 The bayes status nnnn and bayes accepted nnnn Files 8 5 5 1 The bayes model nnnr Fil s ics s s sebo aada onn eaaa 8 5 6 The bayesssummaryl nnnn File tiaa ead 02 eee 8 5 7 The bayes ssummary2 nnnn Piles a accs csta t esasta ddod ee eee 8 5 8 The bayessummarys nnnn Bie 22 2 t t x R3 Ey 8 6 Bayes Analyze Error Messages eh 9 Big Peak Little Peak 9 1 The Bayesian Calculation lacio Oe OE Rm a UR ORE a e RC RCRUS 9 2 Outputs From The Big Peak Little Peak Package leen 10 Metabolic Analysis 10 1 The Metabole Model 2 222299 mom mo RK KARE eGR MEA ww REESE 10 2 The Bayesian Calculation oa cir see A OE eR ee Y s 10 3 The Metabolite Models
37. Bayesian Analysis Users Guide Release 4 00 Manual Version 1 G Larry Bretthorst Biomedical MR Laboratory Washington University School Of Medicine Campus Box 8227 Room 2313 East Bldg 4525 Scott Ave St Louis MO 63110 http bayes wustl edu Email larry bayes wustl edu August 21 2013 Contents Manual Status 1 An Overview Of The Bayesian Analysis Software Ll The Server Software second naw eee eR Gea an CP Pee ee 1 4 463 12 The Client Interiace lt i sone m Romo m HRA aaa A A AR 1 2 1 The Global Pull Down Menus ccr m da EE la 1 2 2 The Package Interface 266 voe Ro sema m x 3 E Re s 1 2 9 The Viewers 6 4 60 ob ok owonchom mox bode dee nee ee ada OX R44 4 4 43 2 Installing the Software 3 the Client Interface 2I The Global Pul Down Men s Rom T oy eee eee SEA s l Ahe Piles mend o e ARA OX a RA 351 2 the Packages Me o 2o v wv AAA WX S oos A9 the WorkDir MENU saxo REDE S 9 ow SHER RRS OSS Row mew d Sled the Settings Mend oso noria 3o odo rot ok RR XX Ee pops 21 9 the D bbiesdBeHU uon Rom SA C 8 OR 8 9 X Aw Bl MR Dee Alb wire Help mel ulna a a a SOUS mde a qe AUR ee e RRE 3 2 The Submit Job To Server ar a 449 Las oe ey ow 4 3 3303 9 3 VR es mu The Server ares fa seek ke GG Rue oe dem m LAUR E RM AU ORE EE ue 24 Interface Viewers i qe go eo oe e OA EEE ee RAO Ao Y OC 34 1 the Asci Data Viewer o 9 442 24444455565 8 Be mom eg RO dede ae the Bd Data Viewer s a Resume BS 3
38. For a complete description of the log file see Subsection 8 5 4 Output the output file is a detailed output from every model processed by Bayes Analyze For a complete description of the output file see Subsections 8 5 2 Model the Bayes Analyze model file is used as input to Bayes Model Bayes Model takes the parameters in the model file and generated an fid model of the Marquardt fid For a complete description of the model file see Subsections 8 5 5 1 Status While Bayes Analyze is running it updates a status file with some information about what it is currently doing This information is written into a status file that is fetched by the status button For a complete list of the various status messages see Subsections 8 6 86 THE CLIENT INTERFACE Summary 1 When the summary 1 report is run it goes into the Bayes Output file and locates the model which had the highest posterior probability and then writes that model into the summary file For a complete description of this file see Sections 8 5 6 Summary 2 When the summary 2 report is run it goes into the Bayes Output and Bayes model files and locates the model that had maximum posterior probability and then produces a summary of the report For a complete description of the summary 2 file see Sections 8 5 7 Summary 3 or the regions report is produced whenever a regions file is present in the BayesAnal ysisFiles directory When present the scripts will run the summary 3 report For a
39. Fortran C Code Editor shown here is used to edit your currently selected model In this popup window the text can be modified in any way you please You can add parameters change the number of model vectors as well as edit the parameters and the model and if you activate the Edit Create New Models button both the model and the parameters can be modified in the popup window For a description of how to write Fortran C models see Section E Parameters will display the parameters file associated with this model See the above comment on the code 3 4 10 1 Fortran C Model Viewer Popup Editor To edit a model one activates the Edit Create New Model button in the lower left hand part of the Fortran C model viewer When activated the code is copied into a work file and that file is displayed in the Fortran C model editor shown in Fig 3 4 10 1 On this edit window you can modify the number of parameters delete add derived and change the number of model vectors Here is a rough description of how to do these things Create Edit Model contains the name of the current model If you wish to create a new model simply change the name of the model in this field To save this model you must hit the Save THE CLIENT INTERFACE 89 and Load button Abscissa can be used to set the number of abscissa columns Remember if you change the number of abscissa columns the code will probably need to be modified to accommodate this change Data Columns ca
40. Fortran lst will display the file BayesHome WorkDir model compile CurrentModel lst where Cur rentModel is the name of the Fortran of C model loaded Note that this listing will contain any errors issued by the Fortran or C compilers when the Build button is activated Note that if you were to use the File Viewer to look at the contents of a WorkDir after it has been successfully run you will find that it contains many more files than mentioned here Those other files contain the probability density functions and the other reports mentioned earlier in this Section As noted the Text Viewing area allows you to view the output from the current model but it also lets you view the Bayes Analyze output from the previous run of Bayes Analyze This selection menu also contains a fixed number of entries Activating each entry will do the following 84 THE CLIENT INTERFACE Parameter Name Mean StdDev Peak BayesExpGiven Rate_1 1 63255E 03 1 47866E 03 2 22598E 05 BayesExpGiven Rate_2 2 95738E 01 6 03008E 03 3 01355E 01 BayesExpGiven Time 1 4 44296E 03 5 02856E 04 4 49241E 04 BayesExpGiven Time_2 3 38280E 00 7 03289E 02 3 31834E 00 BayesExpGiven Amplitude_1 01 1 01643E 02 1 84909E 00 9 97170E 01 BayesExpGiven Amplitude_2 01 1 01287E 02 1 72691E 00 9 94602E 01 BayesExpGiven AmpRms Set 1 1 43493E 02 2 52340E 00 1 40840E 02 BayesExpGiven NoiseStdDev 01 1 08257E 00 8 47944E 03 1 07244E 00 BayesExpGiven Amplitude_1 02 1 00316E 01 1 80558E 01 9 843
41. I Rate_2 360 Time_1 365 Time_2 370 Amplitude_1 Set1 375 Amplitude_2 Set1 380 J Constant Set 1 385 1t L AmpRms Set 1 390 es NoiseStdDev Set 1 99533 A 400 Rate_1 vs Rate_2 TS 405 Log Probability 8 40 415 p 420 38 425 tt 430 g 435 440 V 2445 450 455 460 465 470 475 480 j 485 4 490 495 e 500 Get MaxEnt Histogram Ros ES 0 00 0 05 0 10 0 15 0 20 0 25 0 30 0 35 0 40 0 45 View Samples Beta eu Figure 3 25 When the Markov chain Monte Carlo simulations run the intermediate results can be used to compute the logarithm of the posterior probability Additionally a plot of the expected logarithm of the likelihood can be produced This plot can be used to aid one in determining if the Markov chain Monte Carlo simulations have converged THE CLIENT INTERFACE 77 Given and Unknown Number of Exponentials File Package WorkDir Settings Utilities Help Submit Job to Server Server acd Analysis Option n Ptas EIj gt zmm RUN jl Cancel Set Jl Status Set Order 2 J Find Outliers G Save Get Job Run bmrw200 Include Constant Reset Ascii Data Viewer FID Data Viewer Image Viewer Prior Viewer Fid Model Viewer PlotResults viewer Text Results Viewer File Viewer Output Plots Scatter Plot of Rate_1 vs Rate_2 Data Model and Resid Set1 bes ii iis i i he pv j Data and Model
42. Monte Carlo samples This is illustrated here the peak of the histogram is rather different from the sample that had maximum posterior probability THE CLIENT INTERFACE 75 probability is somewhere around 0 094 So be warned the peak in the histogram and the sample that had maximum posterior probability can be very different 3 4 7 1 the Expected Log Likelihood Plot A plot of the expected logarithm of the likelihood as a function of the annealing parameters is shown in Fig 3 25 When the Markov chain Monte Carlo simulations start the annealing parameter labeled Beta starts at zero and is increased to one according to some annealing schedule The Markov chain Monte Carlo simulations are being done using simulated annealing In simulated annealing one raises the likelihood to a power 8 If the parameters of interest are designated by M and the data as D then logarithm of the posterior probability is given by log P M DI log P M I Blog P D MT 3 8 where P M DI is the posterior probability for the parameters given the data and the prior informa tion P M I is the prior probability for the parameters 8 is the annealing parameter and P D MI is the direct probability for the data given the parameters M and the prior information and in this discussion it is called a likelihood When the annealing parameter is zero only the logarithm of the prior probability contributes to the calculation and the simulations explore the prior proba
43. Peak Bayes Find Resonance Bayes Metabolite Behrens Fisher Errors In Variables Given Polynomial Models MaxEnt Histograms Binned Histograms Bayes Phase Bayes Phase Nonlinear Analyze Image Pixel Image Model Selection 37 The package menu allows selection the of the package to be run When activated the menu lists all available packages The packages are grouped more or less by the type of data and model processed For example Exponential Inversion Recovery and Diffusion Tensor all process ASCII data and they all process models that are exponential in nature while things like Bayes Analyze Big Peak Little Peak Find Resonance and Metabolite analysis all analyze fid data and they all estimate parameters associated with resonances A brief description of each package is given in this section and a Chapter is devoted to describing the models and in some cases the Bayesian calculations done in each package Figure 3 4 When the Package menu is selected this pull down menu is displayed It is populated with a complete list of all of the packages supported by the Bayesian Analysis software Selecting a package will cause the interface to display the interface to the selected package and the interface will configure the current working directory for that package 38 THE CLIENT INTERFACE 669 values or g gradient values for the abscissa and the b values can be either 3D vectors or b matrices Thus this package pro
44. RESTORE ANALYSIS Bayesian Analysis of Common NMR Problems Developed at Washington University in St Louis Mallinckrodt Institute of Radiology Bayesian Analysis Software developed by Java Interface developed by Larry Bretthorst Ph D Karen Marutyan Ph D Research Associate Professor of Radiology Post doctoral Researcher Washington University St Louis MO Washington University St Louis MO gbretthorst wustl edu marutyan wustl edu SEs Figure 3 1 The Bayesian Analysis Start up Page allows you to select what functions you wish to perform For example you might restore an old analysis change a setting run one of the utility programs or select a new WorkDir or a new Bayesian Analysis package THE CLIENT INTERFACE 31 Package WorkDir Settings Utilities The Files menu can be used to Load ASCII files from multiple sources Load Ascii Load Spectroscopy Fid gt Load reia fid from Varian Siemens Load Image Load Image from ASCII fdf dicom 4dfp and Load Abscissa ima files Download Test Data Load Abscissa for image processing Download Manual pdf Download Test Data to the current Bayes Save Working Directory Home directory Import Working Directory Download Manual pdf download this man import Working Directories in Batch ual to the current Bayes Home directory Exit X4Q Save Working Directory saves the current WorkDir to a location of your choosing Import Working Directory reloads a saved Wor
45. Set 1 Varr po po H8 1 1 Tg 1 i TM Residuals Only Set 1 1111 F pee eese H F id iecur imas E RIAS ks REDE GER Rate 1 14041 dics m Moser A E eccesso sen Eun i Rate_2 1 09 j o Time_1 1 08 i Time_2 1 07 i i i b 4 H i E ook i 8o d n cb Amplitude 1 Set1 1 06 Ji Ead i EI i j i SENI j O ere A RC ED Amplitude_2 Set1 Constant Set 1 ue AmpRms Set1 uel NoiseStdDev Set 1 4 55 Log Likelihood gt i Rate 1 vs Rate 2 1 01 Log Probability 1 00 4i e 0 99 2 0 98 Ig 0 97 0 96 0 95 0 94 0 93 0 92 0 91 0 90 0 89 t 0 88 0 87 0 86 0 85 1 1 d E SaR lc i owal o i Get MaxEnt Histogram 0 82 i i if i i i d ec wr cell e ili i bs i i i View Samples 0 18 0 19 O20 0 21 0 22 023 0 24 0 25 026 O27 0 28 029 0 30 0 31 0 32 0 33 0 34 0 35 Rate 1 ej ua Figure 3 26 When the Markov chain Monte Carlo simulations run many of the packages output scatter plots that are used to determine if the parameters are correlated and to check on the con vergence of the simulations Here is an example scatter plot created using the exponential package with biexponential data with a constant The plot is of the two decay rate constants one verses the other In this case there is a strong correlation between decay rate constants but the simulations are otherwise well converged 78 THE CLIENT INTERFACE joint posterior probability for the decay rate constants In Fig 3 26 the sca
46. TERFACE Auto Range will automatically set the range to view the entire spectrum in both the horizontal and vertical domains 3 4 3 Image Viewer Image data can be loaded into any package using the File Load Image menu As explained in Section 3 1 1 many different types of image can be loaded and these images are converted into 4dfp images and stored in the image Subdirectory A 4dfp image consists of multiple binary images that are stacked by slice and element number Multiple images can be loaded provided they have unique names If the names are not unique then the current image replaces the previously loaded image Images are used as input to several packages and can be viewed using the Image Viewer The Image Viewer is is shown in Fig 3 16 In general terms this viewer consists of four parts a list of images under the Image List label two sliders that allow a particular image in a stack to be selected 3 4 3 1 the Image List area The image list area is used to control what image a 4dfp stack is currently being displayed The image list is just as its name implies a list of currently loaded 4dfp image stacks Clicking on a 4dfp stack will cause the stack to be selected and the image indicated by the slice and element number to be displayed The image within the stack is displayed can be controlled using the sliders at the bottom left of the Image Viewer The currently selected image stack is highlighted in red and the check box
47. X3 eee UR b Rus 3 59 Image Viewer 22592299 WA RO x ox o Ro x A Roy x wo 34 31 the Image List Area 2x 46g roe t k o a ee EE S432 the Set Imag area 222 kG S m Ru ook S 34 9 9 the mage Viewing BPO pg 666 64 a ye ed UE E REX ew we S 3 4 3 4 the Grayscale area on the bottom odo he Pizel Mioarei ong 9 xRoxoeox AAA A EEE eS 3 4 3 6 the Image Statistics area sore RA 29 14 Prior Viewer 22 Such a RA A dem EORR dns 24 5 tid Model Viewer coord ED deir e RR GO o ee is 24 5 The tid Model Formato c cox koc ReROGR kr Rb RR memos 14 17 17 22 22 25 34 5 2 The bid Model Reports gt o oo ba ew ee ee es 67 9 45 Plot Results Viewer coccion dod ol d hse 244 ee eee 3 68 3 4 6 1 the Data Model and Residuals Plots 70 34 62 the Posterior Probabilities Plots sa eera 22224284 ee 94 71 3 4 7 the Posterior Probability Vs Parameter Samples plot 72 3 4 7 1 the Expected Log Likelihood Plot 75 34 12 the Scatter Plots 2 420 606 ee RR b omo 9o e eee ee 75 34 5 9 the Log Probability Plot 2 24404 44 4 464404 sad a I x d s 78 3 4 8 Text Results Viewer coace s macaa oon 08084445 ao Lees 80 3419 Res Viene pois Oe X ux uec e ch ou ORES ees 86 3 410 Fortran C Gode Viewer 444466 66 oe RR REESE SP 86 3 4 10 1 Fortran C Model Viewer Popup Editor 88 An Introduction to Bayesian Probability Theory 91 4l The Rules of Probabilit
48. and attempt to construct the abscissa from procpar If multiple variables are arrayed in the procpar then a multicolumn Abscissa file is constructed Download Test Data to the Bayes Home directory The Bayesian Analysis software ships with a directory containing data that can be used to test the various packages This data is contained in a file on the server That file is located in the Bayes user account in a directory named Bayes The file is named Bayes test data tar gz However the data is not generally accessible to users because the file is a gzip compressed tar file When selected the Download Test Data submenu downloads a copy of this file and then uncompress and untar the files The directory Bayes test data containing the test data is placed in the Bayes directory in the bayes user account The downloaded test data can then be load and used to test the various packages Inside the Bayes test data directory the test data is organized by package Download Manual pdf will download a copy of the user manual to the Bayes Subdirectory in the current Bayes Home directory This manual is named BayesManual pdf and is the version of the manual issued with the Bayesian Analysis software installed on the server Additionally a web browser can be pointed to http bayes wustl edu Manual BayesManual pdf and the most recent copy of the manual can be downloaded from the Bayesian Analysis home page Finally the above link can be activat
49. at there are some rather complicated rules concerning what Ascii files can be loaded in a given package To give one example in the exponential package only load two column Ascii files can be loaded while in the magnetization transfer packages only load three column ASCII file can be loaded Additionally files suitable for the the magnetization transfer packages will not load in the exponential packages and vice versa i e the file loading popup knows how many abscissa and data columns are required for a given package user define model For the exact requirements for each package see the Chapter on that package When an Ascii data set is loaded the data is copied into the BayesOtherAnalysis directory of the current WorkDir and the data set is renamed as 001 dat 002 dat etc where the assigned number is just the number of the loaded Ascii data set The data sets are renamed with unique names to prevent name collision problems The original name size number of columns are stored in a file named 001 afh 002 aft etc These Ascii file header files the afh files are used to display information about a Ascii file When an Ascii data set is successfully loaded the Ascii Data Viewer Fig 3 12 is automatically activated Additionally it can be activated by clicking the Ascii Data Viewer button When activated a list of all loaded Ascii data files is shown on the left hand side of the viewer When a left hand file name is selected by clicking on it
50. ata 68 THE CLIENT INTERFACE Horizontal is the plot shown in Fig 3 19 In this plot the data model residuals and the individual resonances are all plotted on the same scale If examine Fig 3 19 is examined it is almost impossible to distinguish the data and the model because they overlap each other almost perfectly The residuals are the small randomly varying trace in purple Note that these individual resonances do not actually reach the top of the spectrum in any of the peaks None the less sum of these resonances fit the data perfectly Stacked is a plot of all traces in the model fid one above the other So the lower three traces are the data model and residuals and traces 4 through the top are the individual resonances in increasing frequency order The type of data used in the displayed report is controlled by the data type widget So for example by setting the data type to fid the report type widget will display all of its reports in the time domain Similarly if the data type is set to Spectrum Real then the reports use the real part of the spectrum of the model 3 4 6 Plot Results Viewer The Plot Results Viewer is for all practical purposes the Ascii Data Viewer described in Section 3 12 and everything said about the Ascii Data Viewer applies here In this Subsection we are going to discuss the differences between the Ascii Data Viewer explain briefly how to use this viewer and give a general introductions to the k
51. ata The interface uses the Ascii Model Files to generate a fid Model Assuming Bayes Analyze Model files are present when one clicks on the Build BA Model fid button or one enters a fid trace number in the entry box then the interface sends a request to the current server to build a fid Model The interface waits for this job to run If needed the user is prompted for a password When the job completes it is automatically retrieved by the interface and unpacked The model fid is Fourier Transform and displayed in the Fid Model Viewer see Fig 3 19 for an example of the output The Fid Model Viewer displays a number of traces one each for each trace in the model field The model fid is a time domain arrayed fid contains the following traces Trace 1 is the complex time domain fid data from the original input fid i e the spectroscopic fid data that is being modeled Trace 2 is the complex time domain fid model of the input fid Trace 3 is the complex time domain difference between the model and the fid This difference is usually called the residuals The remaining traces are the complex time domain models of each individual resonance in the model The resonances are in increasing frequency order so trace 4 is the most negative frequency and the last resonance is the most positive If the total number of resonances if N then the Model fid file contains 3 N traces 3 4 5 2 The Fid Model Reports Next to the Trace spinner on th
52. ata Viewer this viewer also responds to a right mouse click This is true for the plotting area and the Output Plots area However the menu shown in the plotting area is the same as in the Ascii Data Viewer but the menu shown in the Output Plots differs Here is a brief description of this submenu and what it does Plot Information will display all of the information available to the interface about this plot Figure 3 21 is an example of what is displayed when the plot information menu item is selected We have numbered the lines in this figure to make referencing them easier Line 01 indicates that this is a line plot and we are to plot column 1 vs 2 from the file named in Line 03 Line 02 is an internal indicator and it tell us that column 1 of the Bayes Mcmc Samples file is to be THE CLIENT INTERFACE 69 Given and Unknown Numberof Exponentials ja Host bayes File Package WorkDir Settings Utilities Help Submit Job to Server Server Model Analysis Option SaveReset r n RUN Cancel Set Status Set Order 2 i Find Outliers O Save Get Job R Res et Jo un bmrw204 Include Constant o eset J Ascii Data Viewer FID Data Viewer Image Viewer Prior Viewer Fid Model Viewer J Plot Results Viewer Text Results Viewer File Viewer Output Plots The Data Model and Residuals Set 1 and Resid Set Data and Model Set1 Residuals Only Set 1 Time_2 Amplitude 1 Set1 Amplitude 2 S
53. ay This viewer can be used to zoom in on resonances change the scale phase and many other functions See the text for an extensive discussion of this viewer THE CLIENT INTERFACE 53 This pull down menu allows selection of type of data SPECTRUM REAL to be displayed The options allow the display the fid or the spectrum in a number of different modes FID such as absolute value power spectrum etc The real or absorption mode spectrum is the default SPECTRUM REAL Note that this widget determines the type of data SPECTRUM IMAG displayed but it does not determine the form of the report SPECTRUM COMPLEX SPECTRUM AMPLITUDE SPECTRUM POWER Figure 3 14 When the Data Type menu is selected this pull down menu is displayed This menu sets the type of data that is to be output For example selecting fid will cause the time domain fid data to be displayed If a peak is expanded and the Get Peak button is activated the amplitudes of the peaks will be extracted from the current cursor position The interface will attempt to combine these peak amplitudes with any arrayed variable from the fid procpar to produce an Ascii data set that has the appropriate axis This data set is assigned a new Ascii data set number and the Ascii Data Viewer is activated to display the data The Options widget is the most complicated widget on the Fid Data Viewer Its functions are extremely varied and describing all of the functions hidde
54. cepted is the file that is displayed when the Get Job widget is activated and the job has not yet finished The exact contents of this report are specific to a package but in general terms it consists of two parts A header Accepted Report given the ExpTwoConst_Marg model McMC Phase Sampling McMC Simulations 50 McMC Repeats 30 Number Killed Per Cycle 5 Min Annealing Steps 51 Current Step 30 Fraction Samples Gathered 1 00000 Average Log Posterior Prob 3 66274138E 02 StdDev Log Posterior Prob 1 05944 Average Log Prior 19 245 Average Log Likelihood 347 029 StdDev Log Likelihood 1 055 which is reasonably standardized In general terms most of this header is either setup infor mation concerning the package or its a set of current statistics about the current status of the package For example the Simulations Repeats and Minimum Steps are all setup parameters while the others are current status information For example the various average probabilities are the mean value of the given probability averaged across the number of simulations in this case 50 Similarly the StdDev values are the standard deviation of the given probability In general terms the likelihood should increase as a function of the annealing step while the pos terior probability will decrease In both case the standard deviations of these quantities will be large for low values of the annealing parameters and will become smaller as the annealing pa
55. cess 18 different diffusion tensor models Because McMC packages compute the probability for the model using thermodynamic integration this package has the ability to do some simple model selection As with most packages multiple ASCII data sets can be analyzed jointly to look for common diffusion tensor parameters process ASCII Diffusion tensor models similarly for image model selection See Chapter 12 for a description of the diffusion tensor model Enter ASCII Model The Enter ASCII Model package allows the user to define a model and then use Bayesian Probability theory to analyze data using that model To create a simple model activate the Fortran C Code Viewer and then activate the Edit Create New Model button When this button is activated it will make a copy of the Example f model and open it in an editor This model can be changed compiled tested save and run as needed In addition to creating a Fortran C model the users must create a file that describes the model parameters and the prior probabilities for those parameters This process is done simiautomatically when the Fortran C model editor is used However If models are edited manually then this file must be created manually See Chapter 20 for a description of the Fortran C models and their params file Enter ASCII Model Selection The Enter ASCII Model Selection package utilizes the models generated for Enter ASCII to do model selection After setting up a number of riva
56. cessors are available Additionally the number of McMC repetitions can be set and thus the number or samples gathered for use in computing mean and standard deviations parameter estimates The number of samples number of repeats times number of simulations Finally the minimum num ber of annealing steps to take during the the simu lated annealing phase can be set For more on how the McMC is used in the Bayesian Analysis software see Section B Figure 3 8 When the McMC Parameters menu is selected this popup is displayed It allows a number of important parameters concerning the Markov chain Monte Carlo simulations to be configured THE CLIENT INTERFACE 45 ere Setup Servers bayes wustl edu bmrw206 wustl edu The Server Server Setup menu is a popup that allows pri one to add delete and modify server settings To se bmrw204 wustl edu bmrwlas wus edu lect a server simply click on the server name Any pes bmrw200 wustl edu 8080 field except the server name and port number can be login1 chpc wustl edu R te P ina A t P NEWER wind cau emote Processing Accoun modified Servers can be added using the Add Server paves button Servers can removed by activating the re User move server button Finally the View Server Installa Email tion Info button will bring up a popup that lists all of None the installation information available on the server Queue None Maximum CPUs 24 Use CPUs 24 Passw
57. containing a se lection list of the current servers Selecting one of these servers will change the current S S server The Server Name will be changed et tatus to reflect the selection Note selecting the Edit button in the server list will bring up the Server Configuration popup discussed in bmrw208 i PRESE Subsection 3 1 4 Status will send a request to the selected server asking for its current CPU load This system load is displayed using ps on most Linux systems Server Name contains the name of the currently selected server Figure 3 11 The Server Widget Group is used to setup change or to check the status of a server 3 4 Interface Viewers Just below the widget groups is a set of buttons that activate various viewers These buttons start on the left in Fig 1 2 with Ascii Data Viewer and end on the right with File Data Viewer Each viewer is used to look at a given type of data On the Exponential package there are seven of these viewers and this is pretty typical of all packages 3 4 1 the Ascii Data Viewer Ascii data can be loaded and viewed in all packages even packages that analyze fid and image data The Ascii Data Viewer shown in Fig 3 12 is used to display this data To load an Ascii data select the File Load Ascii File submenu item When activated this widget will bring up a popup file loading widget Navigate to the desired file and then select and load the file Please note th
58. culation should not be used as an estimate of the noise standard deviation In a ROI containing only noise the Mean value is part of the noise and should not be subtracted when calculating the noise standard deviation Additionally even in an Absorption mode image this calculation may not give a good estimate of the noise standard deviation again because the deviation form the mean is not an estimate of the noise value RMS contains the Root Mean Square deviation of the selected region Again if p stands for the ith pixel in the selected ROI containing N pixels then the RMS value is calculated as RMS Note for absolute value images this calculation should give a better estimate of the noise standard deviation and in absorption mode images this is the correct was to calculate the noise standard deviation Pixels contains the total number of pixels in the ROI Finally there are three buttons at the bottom of the Image Statics area that are used to get and save various statistics computed by the interface Get Statistics will generate the statistics from the selected ROI If no ROI is present then the statistics are generated for the entire image Note this widget does not use the minimum or maximum pixel values set by the Get Threshold Statistics button it simply computes the statistics for all pixels contained in the ROI Get Threshold Statistics will generate statistics for the selected ROI using a minimum and max
59. d Data Astrophys ical and Space Science 39 pp 447 462 418 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 BIBLIOGRAPHY Loredo T J 1990 From Laplace To SN 1987A Bayesian Inference In Astrophysics in Maximum Entropy and Bayesian Methods P F Fougere ed Kluwer Academic Publishers Dordrecht The Netherlands Malloy Craig R A Dean Sherry F Mark H Jeffrey 1988 Evaluation of Carbon Flux and Substrate Selection through Alternate Pathways Involving the Citric Acid Cycle of the Heart by 13C NMR Spectroscopy Journal of Biological Chemistry Vol 263 No 15 pp 6964 6971 Malloy Craig R A Dean Sherry F Mark H Jeffrey 1990 Analysis of tricarboxylic acid cycle of the heart using C isotope isomers American Journal of Physiology 259 pp H987 H995 Merboldt K Hanicke W Frahm J 1969 Self diffusion NMR imaging using stimulated echoes Journal of Magnetic Resonance 64 3 pp 479 486 Metropolis Nicholas Arianna W Rosenbluth Marshall N Rosenbluth Augusta H Teller and Edward Teller 1953 Equation of State Calculations by Fast Computing Machines Journal of Chemical Physics The previous link is to the Americain Institute of Physics and if you do not have access to Science Sitations you many not be able to retrieve this paper Neal Radford M 1993 Probabilistic Inference Using Markov Chain Mo
60. del Interface 222224 330 Ascii Model Selection Interface eooo ss zo o m kk RR RR R4 4n 332 Absorption Model Images iue no o9 ons Ox WO 9o mUR RR ROX RO E E E E 334 Bayes Phase Interface osos mon ox a 335 Bayes Phase Listing 2 44 4 4 xk OX x X X e AEE MR OX E a a a 341 12 24 1 24 2 28 1 A 1 p D 2 D3 E 1 E 2 Ea E 5 E 6 G 1 Hl H2 Nonlmear Phasing Example a SG ee wx hok buo cod ox AY X 9 5 344 Nonlinear Phasing Interface og essu mona ces kA RR e 348 Image Pixels Example 3444 6 ee ee Rufo ded orc AR S AUS Sex SOR 362 Ascii Data File Format Se a bx RR RUBENS ee eS SEE 368 The McMC Values Report Header o e 02000002 386 MeMC Values Report The Middle A e 22 2222 387 The McMC Values Report The End o o 388 Writing Models A Fortran Example e 392 Writing Models A C Example e 393 Writing Models The Parameter File a 395 Writing Models Fortran Declarations o o naci a a ei aa a a a a o a e a a a a 399 Writing Models Fortran Example eee 402 Writing Models The Parameter File so s sa cci audda enana iadaaa 403 The FD File Header 225492299 RR ee A XR Pee RRA 409 the Posterior Probability for the Number of Outliers a a ouaaa aaa 412 The Data Model and Residual Plot With Outliers lll 414 List of Tables 8 1 Multiplet Relative Amplitudes eee eee eee
61. depending on the type of terminal in use This menu allows the size of the window to be set without using a mouse Preferences The preference widget will bring up a popup that allows you to configure some prefer ences The main settings are for the location of the Bayes Home directory You can uninstall the Java interface from you server You can tell the interface what output format to write screen captures in Finally there are a couple of widgets that indicate if jobs are to be deleted from the servers This last function is mostly used by us in debugging software It could happen that while trying to diagnosis a problem we need for the job to remain on the server so we can see what happened to it Normally completed jobs i e any job that is no longer active on the server are removed as soon as the get job widget is activated 3 1 5 the Utilities menu The utilities menu allows the user to run a number of utilities These utilities can monitor the memory usage display some information about Java and its instillation and finally determine if a new version of the software is available Here is a more detailed description of these utilities There are three utilities that can be run by the user Memory Monitor will activate a Java Memory monitor Java for whatever reason normally can only access 1GB of memory Sometimes we have found that this is not enough to hold large images and applications The memory monitor can be used to monitor memo
62. description of how to generate a regions file see Subsections 3 4 2 For a complete description of the summary3 report see Sections 8 5 8 Regions will list the regions file if it exists For a description of how to generate a regions file see Subsections 3 4 2 For a complete description of the regions file see Sections 8 5 8 3 4 9 Files Viewer The Files Viewer is a tool provided to assist you in finding files When activated the viewer opens in your current Bayes Home directory and it shows you a listing of all files and directories in Bayes Home Using a single mouse click on a file will display that file while using a double mouse click on a directory will expand that directory You can use this tool to quickly locate and display files Note that as of this writing a variable length font is in use by this viewer and consequently it does not preserver line spacing when a file is displayed 3 4 10 Fortran C Code Viewer The Fortran C Code Viewer is shown in Fig 3 30 it is used to view and or modify the Ascii models you have loaded When a model is loaded using either the System or User buttons a local copy of the model is stored in the BayesAsciiModels subdirectory of your current Bayes home directory and it is displayed in in the Fortran C Model Viewer along with a list of all of the currently loaded models left panel This viewer contains 5 total widgets and here is a description of them Ascii Models is a list of all of
63. e Y THE CLIENT INTERFACE Data Info will display information bout the fid Save As Varian fid will save the current fid in Varian format Save As Text will save the current fid in Text for mat Show Plotted Data will popup the data in a Text browser Clear Data will delete the current fid Apply Phasing will popup a phasing widget Set Regions will popup a regions setting widget Set Fn will set the FT size Set Ib will set the line broadening value Set Reference will popup a referencing setting widget Set Units will allow the units to be changed Properties allows some plotting preferences to be set Copy copies the current image to the clipboard Save As popup a save widget Print popguns a printing widget Zoom In allows the image to be zoomed in Zoom Out allows the image to be zoomed out Auto Range fits the data to the display window Figure 3 15 When the Options menu is selected this pull down menu is displayed It performs various optional tasks concerning the Fid Data Viewer For example the size of the Fourier transform the weighting or reference on the Fourier transform can be set etc THE CLIENT INTERFACE 55 Apply Phasing will bring up a popup window that allows the phase of the currently displayed fid to be set This popup contains two sliders that allow the zero and first order phase to be set The displayed fid can be zoomed using the procedures described earlier in Section 3 4 1 so
64. e Model Fid Viewer there is a widget that is initialized with the work Trace in it This widget is the Report Type widget and the word Trace refers to the fact that the default report is to display the model traces The report type widget is actually a selection menu and when activated it will display a selection of different kinds of reports that can be viewer printed etc This report type selection menu has the following selection items Trace is a display of the individual traces in the model fid The trace spinner just to the left of the report type selection menu can be used to change the trace number The number can also be changed by typing in the trace number to be viewed Data will display the original fid data As noted the format of the fid data is also controlled by a selection menu The default data type is to display the spectrum of the data Model will display the model fid data Residual will display the difference between the complex fid data and the model Vertical will display three plots stacked one above the other the bottom plot is the original fid data the middle plot is the model fid and the top plot is the residuals Again the format of these displays is controlled by the data selection menu menu Overlay also displays the data in three stacked plots Here the lower plot is the original fid data overlaid by the model The middle plot is the residuals and the top plot is a plot of each resonance in the d
65. e a edit window however you can use the parameter window to edit the parameters First you can change the parameter being displayed along the top in two ways You can simply left mouse click on the parameter you wish to view or you the down arrow on the right hand side of the displayed parameter name can be used to select a parameter Regardless after selecting a parameter you can use change any value displayed in the top line As you change these values the pa rameter file is automatically updated There are about nine different fields displayed for each parameter here is a brief list of their functions Name is the name of the current parameter You can simply enter another name if you wish to change this Note that names must be unique within a model Low is the lowest value the parameter can take on Simply enter any value you wish to change the low value Note that you can enter any value in this low field including something larger than the high and the popup will not complain However such errors must be corrected before you will be able to save the prior Mean is the mean value of the Gaussian prior and this filed is also used as the peak value in a positive prior Note that this editor does not change the labels on the prior fields when the priors types are changed High is the highest value this parameter can take on and is used by all priors Sdev is an abbreviation for Standard Deviation and is used on Gaussian Prior probabilitie
66. e2 eee 44 cee 04454 ES The Subrodtie Body 222229 5309 2x39 m mo 48 9 box s E 6 Model Subroutines With Marginalization F the Bayes Directory Organization G 4dfp Overview H Outlier Detection Bibliography 343 343 345 347 361 363 365 367 367 368 369 375 376 377 378 378 379 380 381 385 391 391 394 396 398 399 400 405 407 411 415 List of Figures 3 21 3 22 3 23 3 24 3 25 3 26 3 27 3 28 3 29 3 30 3 31 The Start Up Window i sosa RA RSA 4 DO 9 3 3 9 4 RE eS 21 Example Package Interface sosa e ee y a EA OE RU XU Y E 23 Whe Start Up WIDdONW es e Seka ee eee a X PPP E A ACE SOR SI see G 30 Tbe Piles Wend 2 uo eu eee deemed des o Roh oho RR mene 31 The Load Image Selection Menu o o a Aa A ee eee 33 The Packages Menu 24 4 2 9 9 9999 a a A 37 The Working Directory Pull Down Menu o 42 The Working Directory Po pup ceo 444 604 aaa daa taaa ateo m RES 43 The Settings Pull Down Menu ee 44 The McMC Parameters Po pup 2 02 42 LES ee See RBAUS os 44 The Edi Server POPUD cs rama 4 YA Wank Rs ee ce SS box xk OES ow 45 The Submit Job Widget Group eo mmm tbe he pee atta eui 9 Ee me n 48 The Server Widget Group cnc Behe eae a DAA AAA 49 the Ascii Data viewer s sc cora osoa ee 50 the tid Data viewer uu c a aralara ee eee ee Eee eee ee es 52 The Pid Data Viewer Display Type o ca sra sunud 044444 24 Ry 53
67. eak Pick o 254 Magnetization Transfer Interface bia a a E a a a 256 Magnetization Transfer Peak Pick o oo a a a eee 262 Magnetization Transfer Example Data oea cac errau aa ee eene 263 Magnetization Transfer Example Spectrum aaaea a 264 Magnetization Transfer Kinetics Interface auaa 268 Magnetization Transfer Kinetics Arrhernius Plot llle 274 Magnetization Transfer Kinetics Water Viscosity Table 275 Given Polynomial Order Package Interface o 278 Given Polynomial Order Scatter Plot o aa naaa 284 Unknown Polynomial Order Interface o a a a a a a a a a a lea 286 The Distribution of Models lt s s ecos aa sacas E rto SR diit 290 Unknown Polynomial Order Package Posterior Probability 292 Errors In Variables Interface coo 22cm oO Rn 296 Errors lm Variables McMC Values File 0040544464444 m 4 4444 Seo 302 the Behrens Fisher interface ee 304 Behrens Fisher Hypotheses Tested o eee 305 Behrens Fisher Console Log eee 315 Behrens Fisher Status Listing eee 316 Behrens Fisher McMC Values File The Preamble lll 317 Behrens Fisher McMC Values File The Middle llle 318 Behrens Fisher McMC Values File The End llle 319 Enter Ascii Model Interface o een 322 Test Your Own Ascii Mo
68. eate New Model button is activated The code is displayed in a popup in a popup editing window Finally the Remove Selected Model can be used to delete the model from the your BayesAsciiModels subdirectory Note that activating this button removes your local copy of the model it does not remove the model from the system directory 88 THE CLIENT INTERFACE CREATE EDIT ENTER ASCIl MODEL Model Specifications Lf Code Parameters Compile Result CREATE EDIT MODEL Integer Intent In NoOfDerived Integer Intent In TotalDataValues Integer Intent In MaxNoOfDataValues Abscissa 1 lj Integer Intent In NoofDataCols Datacolumns 1 Integer Intent In NoOfAbscissaCols Model Vectors 0 Integer Intent In NoOfModelvectors En E Real Kind 8 Intent In Params NoOfParams Real Kind 8 Intent Out Derived NoOfDerived Derived d i y Real Kind 8 Intent In Abscissa NoOfAbscissaCols MaxNoOfDataValues Real Kind 8 Intent InOut Signal No0fDataCols MaxNo0fDataValues COMPILE ON SERVER Integer CurEntry CANCEL AND EXIT Real Kind 8 Rate AmpZero AmpInfty SAVE AND LOAD Rate Params 1 AmpZero Params 2 AmpInfty Params 3 If Rate Eq 0D0 Then Derived 1 ODO Else Derived 1 1d0 Rate EndIf Do CurEntry 1 TotalDataValues Signal l CurEntry AmpInfty AmpZero AmpInfty Exp Rate Abscissa 1 CurEntry EndDo Return End Figure 3 31 The
69. ecific i e the number of data and abscissa columns required varies with the package The file format for each package is addressed in the Chapter describing the package However the general file format used by Bayesian ASCII software is described in Section A After the data is loaded into the WorkDir the ASCII Data Viewer is then activated and the ASCII data is plotted in the viewer 32 THE CLIENT INTERFACE The Load ASCII menu has two submenus one to load a plain ASCII file and one that extracts amplitudes from a Bayes Analyze file Here is a description of these selection menus File brings up a navigation popup that navigates to the appropriate ASCII file and then load that file Note that file is parsed by the interface to determine if it has the correct number of data columns and that it contains only ASCII data The loaded ASCII file is copied into the current WorkDir and the file is assigned a name using a sequential number These numbers are unique so multiple ASCII files having the same name can be loaded without conflict The loaded file is then displayed in the ASCII Data Viewer Bayes Analyze File is a selection menu that will load the amplitudes of a resonance as a function of some arrayed parameter These amplitudes are read from the previous run of the Bayes Analyze package A prompt for the resonances number who s amplitudes are to be loaded will appear The Bayes Analyze analysis must use a joint analysis i e all fid
70. ed and the acrobat reader will download the most recent version of the manual from bayes wustl edu Save Working Directory widget allows a WorkDir to be saved When this widget is activated a popup is displayed This popup allows selection of both the WorkDir and the location where the WorkDir is to be saved Finally the WorkDir is copied to the specified location When the WorkDir is copied the entire contents of the WorkDir are copied all ASCII files images fid s etc are copied and saved in the specified location 36 THE CLIENT INTERFACE Import Working Directory allows a saved WorkDir to be reloaded When the Load Working Directory widget is activated a popup is displayed that allows the select the WorkDir to be reloaded In a copy statement this is the source location of the files to be copied After selecting the source WorkDir you are prompted to enter the name of the WorkDir where the files are to be copied will appear The source directory is then copied to the Bayes directory in the current Bayes Home using the new WorkDir name as the to location in the copy After reloading the WorkDir plots text reports fid s images and ASCII files will have been restored to the same status they were in when the WorkDir was saved Import Working Directories in Batch imports multiple saved working directories For exam ple while working on a project where model selection was needed on about 100 different sam ples We created a working
71. ede CO ORE EGE RR Eee eRe 191 The Big Peak Little Peak Interface 2 2 0 maa eee ee ee ee 198 The Time Dependent Parameters o 0020002 e e 208 The Bayes Metabolite Interface o e e ee ee 210 Bayes Metabolite Viewer ao arad iape kaa a aa aa a E A 212 Bayes Metabolite Probabilities List o oea cna saraa e a 217 The IPGD D20 Metabolite ecos 3399 Romo Be ee dee R E eee eee eee 219 Bayes Metabolite IPGD_D20 Spectrum e o 220 Bayes Metabolite The Fraction of Glucose o 221 Glutamate Example Spectrum coccion eee ds 223 Estimating The Foo y and Fag Parameters eee eee eee 226 Bayes Metabolite The Ethyl Ether Example 227 12 1 12 2 12 3 13 1 13 2 13 3 13 4 14 1 14 2 14 3 14 4 15 1 15 2 15 3 16 1 16 2 17 1 172 17 3 18 1 18 2 19 1 19 2 19 3 19 4 19 5 19 6 19 7 20 1 22 1 23 1 23 2 23 3 the Find Resonances interface 2A 230 Difusion Tensor Interfate u lt lt aa eee Roe e SR XU ATE Res 238 Diffusion Tensor Parameter Estimates ea eens 246 Diffusion Tensor Posterior Probability For The Model 246 The Big Magnetization Package Interface o 250 Big Magnetization Transfer Example Fid cesses 252 Big Magnetization Transfer Expansion 0 00 0 ee ee eens 253 Big Magnetization Transfer P
72. el Files that must be further processed to produce a fid model The Build BA Model button builds these fid models from the Ascii Model Files when needed The Fid Model Viewer button is present on all packages and can be used to generate Bayes Analyze models from previously analyzed spectroscopic 66 THE CLIENT INTERFACE Bayes Analyze test2 Host bayes ene File Package WorkDir Settings Utilities Help Submit Job to Server Server Constant Models Settings Set Traces Set Signal Noise Mark Resonance 1 i Shim Order None v From 1 m RUN Cancel Set Status Q First Point poo Signal 1024 Primary 1 Q Real Offset Max New Res 10 Te 1 me Get Job Run bmrw208 Q Noise 0 Secondary Y J J Imag Offset Phase e By 1 J Number of resonances 9 4X TJ 7 Ascii Data Viewer ro Data Viewer Image Viewer i Fid Model Viewer Plot Results Viewer Text Results Viewer File Viewer SPECTRUM REAL x Options Build BA Model For FID FREQUENCY PPM CursorA CursorB O gt aj zx Figure 3 19 Frequency finding programs have the ability to display their outputs overlaid by the original fid These outputs can be in the time domain or in the frequency domain Additionally because fid data can be arrayed displaying these outputs requires a special Viewer to generate and display the results This is the job of the Fid Model Viewer shown here THE CLIENT INTERFACE 67 fid d
73. eleted 44 WorkDir Utilities Help Server MCMC Parameters Server Setup Set Window Size Write Log Files Threshold image pixlel Data Images Priors Viewer Fid Model Viewer THE CLIENT INTERFACE The Settings menu is a pull down that allows one to configure and control a number of important fea tures of the interface The two most important set tings concern the McMC parameters and the Server Setup When the McMC Parameters menu is acti vated it brings up a popup that allows the number of simulations repeats and the minimum number of an nealing steps used in the Markov chain Monte Carlo simulations to be set When the Server Setup is acti vated the resulting popup allows one to add remove and configure servers Finally the preferences button will bring up a popup that allows the configuration some interface parameters like for example the loca tion of the Bayes Home directory Figure 3 7 When the Settings menu is selected this pull down menu is displayed It allows one to configure the Markov chain Monte Carlo simulations and to configure a series of users preferences 00 MCMC Markov Chain Monte Carlo settings Simulations Repetitions 55 Min Annealing Steps 35 Cancel OK The McMC Settings menu is a popup that set the number of Markov chain Monte Carlo simulations that run concurrently or in parallel Concurrently if only a single processor is available and in parallel if multiple pro
74. erly configured it will create a tar file of the current WorkDir and send it to the server shown in the server widget group When the job arrives at the server it is untared and then and the requested programs are run After the job arrives at the server interface set the status to either Active or Queued and it will lock most of the widgets on a package The user is free to join another analysis or wait for the analysis to finish Cancel will cancel a submitted job and remove all files pertaining to that job from the server even if the job is completed When finished canceling the job the interface will set the current 48 THE CLIENT INTERFACE z Run will submit a job to the indicated server Submit Job to Server Cancel will cancel a submitted job and remove all files pertaining to a job i C l Get Job will fetch the current job or fetch the sta ance tus of the current job Status Label contains the status of the current Get Job Not Run job Figure 3 10 The submit Job to the Server Widget Group Is used to send and fetch jobs from the servers status to either Not Run or error if the job could not be canceled and or removed from the server Get Job performs two main tasks when activated it first checks the current status of a job and depending on the status it either fetches the job or it fetches and displays the accepted report Text Label contains the status of the current job Note this field is
75. es are read by the interface as series of lines each containing multiple pixels Each line in the file corresponds to one horizontal line in the displayed image For MRI data each line corresponds to the phase encode direction The number of phase encode pixels depends on the number of phase encodes and the zero padd level of the Fourier transform So if the image has a total of 64 phase encode pixels including zero padding then each line in the text file must have 64 phase encode pixels Additionally if there are 96 pixels in the vertical readout direction then there must be 96 total lines for each image in the text file Like single column text files multiple images can be stacked in one file and the images can be ordered by either by slice or array element Also like single column text files when an image is selected a popup will be displayed and the number of slices array dimension and image sizes must be specified Siemens IMA will bring up a popup that allows navigating to loading of of Siemens IMA images One or more of the IMA files can be selected and opened This will copy and reformat the IMA images into a single 4dfp file located in the images Subdirectory of the current WorkDir The order of the images is alphabetical if the images must be ordered in some special way they must be renamed appropriately DICOM will bring up a popup that allows navigating to and loading of DICOM images This will copy and reformat the DICOM
76. esolution than Bayes Analyze See Chapter 11 for a description of the Find Resonance package Metabolite The Metabolite package analyzes fid data from a number of known samples for ex ample a C13 fid of Glutamate The intensity of the Glutamate resonances are related to each other through a metabolic model This model can be very simple or very complex Metabolic models can be added to the library of models but there are no facilities for building these models within the interface Metabolic models relate the intensity of the resonances in the model to a series of metabolic parameters typically fractional rates that relates how much of a compound went through a certain chemical reaction The resonances in a metabolic models are described in a metabolite file and the metabolic model itself is encoded in a FORTRAN or C routine The metabolic package reads the resonance and the metabolic models and then uses Bayesian probability theory to estimate the metabolic parameters as well as the parameters associated with the resonances i e the frequencies and decay rate constants See Chapter 10 for a description of the Metabolite package 40 THE CLIENT INTERFACE Behrens Fisher The Behrens Fisher package solves the classical medical testing problem given two experiments that consist of repeated measurements of the same quantity where in the second measurement one has change some experiential parameter determine if the experiments are the same or if they d
77. et 1 Constant Set 1 AmpRms Set 1 NoiseStdDev Set 1 Log Likelihood gt Rate 1 vs Rate 2 Log Probability Intensity 00 05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 9 0 9 5 10 0 10 5 Get MaxEnt Histogram View Samples Data Model Residuals Figure 3 20 Ascii packages and some fid packages output Ascii Plot files These plots are displayed by the Plot Results Viewer Roughly speaking there are six different types of these plots plots involving the data model and residuals plots involving the posterior probabilities for parameters plots showing correlations between parameters and two types of plots that are used to determine if the analysis ran converged correctly 70 THE CLIENT INTERFACE 01 Line 1 2 02 1 03 BayesExpGiven Rate_1 04 Prob for the Rate_1 Given a 2 Exp Model and a Const 05 Rate_1 06 Rate_1 07 Probability Density 08 Mean 0 26448 Sd 2 15E 02 Peak 0 26487 Figure 3 21 The plot information widget will popup up a window containing information about the currently displayed plot We have numbered the lines in this display to make referencing them easier Line 01 indicates that this is a line plot and that column 1 vs 2 from the file named in Line 03 is to be plotted Line 02 is an internal indicator and it tell us that column 1 of the Bayes Mcmc Samples file is to be displayed should the user activate the View Samples button Li
78. etely that is to say the prior probability is discretizing and the discrete prior is normalized so that the sum over the discrete samples is one The prior is discretized on a 101 step inclusive interval So for example if the prior is an exponential of decay rate constant 1 with a range given by Low and High then the normalization constant is given by High Low dX 3 4 100 ee 101 Norm Y exp Low dX i 1 3 5 i 1 so the prior probability is given by paiar e 3 6 Norm Plugging in zero for the low and 10 for the high the normalization constant for the exponential prior is roughly 10 5 The prior starts at about 0 1 and goes down exponentially by about a factor of 22000 THE CLIENT INTERFACE 63 Build Your Own 1D File Package WorkDir Settings Utilities Help Submit Job to Server Server Load and Build Model Analysis Options ee A Run Cancel set Status system user Find Outliers Get Job Not Run bmrw208 Build Save priors Example_NoMarg f Loaded BUILT Ascii Data Viewer FID Data Viewer Image Viewer J Priorviswer Fia Model Viewer Plot Results Viewer Text Results Viewer File Viewer Fortran C Model Viewer Parameters Positive iv PERES LOW 1 050 Mzlnit PEAK 3 0E0 Mzini p fy HIGH 5 0E1 Prior Probability o o P a 2 la oc o P DecayRatell 5 o t 0 35 0 3 0 25 0 2 0 15 0 1 0 05 4f
79. ewer File Viewer Fortran C Model Viewer Code Parameters Rs ES gt z I Integer Intent In NoofModelVectors Real Kind 8 Intent In Params NoOfParams Real Kind 8 Intent Out Derived NoOfDerived Real Kind 8 Intent In Abscissa NoOfAbscissaCols MaxNoOfDataValues Real Kind 8 Intent InOut Signal NoOfDataCols MaxNoOfDataValues Integer CurEntry Real Kind 8 Rate AmpZero AmpInfty Ascii Models Example NoMarg f Rate Params 1 AmpZero Params 2 AmpInfty Params 3 If Rate Eq 0DO Then Derived 1 ODO Else Derived 1 1d0 Rate EndIf Do CurEntry 1 TotalDataValues Signal 1 CurEntry AmpInfty AmpZero AmpInfty Exp Rate Abscissa 1 CurEntry EndDo Return Remove Selected Model Edit Create New Model O Figure 3 30 The Fortran C Model Viewer shown here is used to view the models you have currently loaded You can change a model by selecting it from the Ascii models list on the left The two buttons Code and Parameters will display the code or the parameters respectively As a reminder the code is either the Fortran or C code used to implement a model and the parameters file contains essentially a description of the prior probabilities for the model The display produced by these two buttons are simple displays and neither the code nor the parameters are changeable on this display However when the Edit Cr
80. ge has been run the various outputs can be viewed using the Viewers The Text Results Viewer is used to view the various reports that are output from the packages The area along the left hand side lists the various reports available from the current package top and from the last run of Bayes Analyze bottom The text has a brief description of the output and you must consult the package Chapter to find out about package specific reports 82 THE CLIENT INTERFACE Probability model will display the contents of the Bayes prob model file This file usually contains one record for each time an analysis package has been run and it contains the results of a thermodynamic calculation for the probability for the model See 55 36 for more on thermodynamic integration Meme Values will display the contents of the PackageName mcmc values file where Package Name is our internal name of a package If you are looking for this file there is only a single file in the BayesOtherAnalysis directory having the suffix mcmc values For a much more detailed description of this report see Subsection D Bayes params will display the contents of the Bayes params file The Bayes params file contains a complete description of the package setup including the prior settings Console log will contain all outputs that went to console when a job is running Usually this is not useful but when something goes wrong the console log would be consulted Bayes ac
81. he histograms are to be smoothed or not See Chapter for a description of the Binned Histograms package Linear Phasing The Linear Phasing package produces linearly phased images In spin echo MRI most images can be phased absorption mode images by calculating two first order phases and one zero order phase Bayes Phase computes these phases and then applies them to the images The resulting images are then available for further processing by the Analyze Image THE CLIENT INTERFACE 41 Pixels package See Automatic phasing of MR images Part I Linearly varying phase for more on this calculation and and for a more detailed description of this package see Chapter 23 Non Linear Image Phasing The Non Linear phasing package phases images that are varying in a Non Linear fashion This package takes as its input the output from the Linear Phasing package This package can be used to produce absorption mode images for gradient echo MR images or any other image in which the phase is varying in an unpredictable fashion For more information on this calculation see Automatic phasing of MR images Part II Voxel wise phase estimation and for a more detailed description of this package see Chapter 24 Image Pixels The Image Pixels package loads a predefined model and then uses that model to analyze images on a pixel by pixel basis Model can be loaded from the system directory and these predefined models perform a number of common calculations in MRI such a
82. his popup are three buttons Set Left Most Frequency to Zero Set Right Most Frequency to Zero and Set Center Frequency to Zero that are preprogrammed common reference schemes To set the reference to an arbitrary value first position the cursor at the point in the spectrum where the reference is to be assigned Second type into the New Value entry box the value of the reference to Finally hit the Set button to set the reference Units is a selection menu that allows the units Hertz or PPM to be set Properties allows the axis and labels on the Fid Data Viewer to be set This can be useful when making a graphic that is to be used in a publication Copy places a copy of the current graphics window and places it on the clip board On Windows and Mac machines this makes the graphics available for plotting and use in papers etc Save As will bring up a popup that allows navigation to the directory where the current graphics is to be saved Enter the name of the file in the File Name box Activate the Save button to save a png copy of the graphics Print will bring up a popup that configures the print jog After configuring the printer the OK button will print the graphics Zoom In will zoom the axis in There are options for zooming either both axis or either axis separately Zoom Out will zoom the axis out There are options for zooming either both axis or either axis separately 56 THE CLIENT IN
83. if a model is selected that requires more than a two column Ascii Data set THE CLIENT INTERFACE 57 Given and Unknown Number of Exponentials test2 Host bayes File Package WorkDir Settings Utilities Help Submit Job to Server Server Model Analysis Option SaveReset RUN Cancel Set l Status Set Order 4 m Find Outliers Q Save Get Job Not Run bmrw208 Include Constant 3 Reset Ascii Data Viewer FID Data Viewer Image Viewer Prior Viewer Fid Model Viewer Plot Results Viewer Text Results Viewer File Viewer List 0 26 mage Lis 0 26 Pixel Info x pos Y pos Value Image Statistics Mean 3 5846e 01 Max 2 9321 e 00 Min 7 4630e 02 Sdev 7 7257e 01 RMS 8 5168e 01 Pix 16384 Getthreshold stats Savestatistics Statistics Readout cm 0 31 0 38 0 46 0 53 Phase Encode cm Slice Number 1 of 1 0 0746300 2 9320977 Element Number UE Oj fix rs Figure 3 16 When the Image Viewer is selected this window is displayed In general terms this viewer consists of four parts the image selection widgets on the left hand side of the viewer The widgets used to select a slice and element on the lower left hand side The image viewing area in the center and the pixel information area on the right hand side of the image For more information on each widget hold the cursor over a widget and read the tool tip 58 THE CLIENT INTERFACE The right mouse
84. iffer See Chapter 19 for a description of the Behrens Fisher package and see On the Difference in Means for a detailed description of the calculations Errors in Variables The Errors in Variables package solves the errors in variables problem In this problem one has a data set that has uncertainty in both the X and Y variables These errors may be know or unknown so this package solves four different errors in variables problems In the name the given refers to the fact that the program solves this problem given the order of the polynomial to fit See Chapter 18 for a description of the Errors in Variables package Polynomial The Polynomial Models package fits polynomials of either a given or an unknown order to the input data When the order is specified then a polynomial of that order is analyzed using Bayesian probability theory to determine the appropriate coefficients When the order is specified as unknown the Bayesian probability theory is used to compute the posterior probability for the order of the polynomials The input data is two column ASCII and this package do not process multiple data sets See Chapter 16 for a description of the Polynomial package when the order of the polynomial is given and see Chapter 17 for the calculations when the order of the polynomial is unknown MaxEnt Histograms The Maximum Entropy Histograms density estimation package is a ASCII package that takes as its input a two column ASCII file Column one is ju
85. ikely result in nonfunctional server configuration The Settings Server Setup popup has four buttons that can be used to add delete configure and display server information Add Server will bring up a popup in which the server name and port number of the server can be entered After entering the server name and port most of the server information 46 THE CLIENT INTERFACE can be configured using the Auto Config Server button However email preferences and user name may have to be set manually Remove Server will delete the currently selected server from the list of servers Note there is no prompt to ask if a server is to be removed View Server Installation Info will bring up a popup that shows more information about the server In will show the date the software was installed the software version the Bayes user account port compiler information including the path to the compilers number of CPU whether or not passwords are in use and information about who the Bayesian Analysis administrator is Auto Configure Server fetches a configuration file from the server It then uses this con figuration to set the processing account passwords and number of CPU on the Server Setup popup Set Window Size will bring up a popup that allows the size of the interface windows to be set Normally one would set the size of the interface by using a cursor to stretch contract the window as needed However sometimes use of a cursor is difficult
86. inds of plots this viewer displays In particular we are going to explaining a few of the more common types plots that show up in this viewer However each package may have plots unique to that package and if a plot is discovered that is not explained here then consult the Chapter on the package being used The Plot Results Viewer is shown in Fig 3 20 and if Ascii Data Viewer is compared to the Plot Results Viewer one will find that about the only difference is the label on top of the plot files list In the Ascii Data Viewer this label reads Ascii Data while here it reads Output Plots In the Ascii Data Viewer the area under this label contains a listing of all of the files that have been loaded into the experiment while here it contains a listing of all of the output plots generated by the package The example shown in Fig 3 20 is the result of running a biexponential model with a constant on biexponential data In the output plots list there are 15 different plots When a plot is activated the output plot list entry is highlighted and the plot is displayed The plots are organized roughly as three groups of plots in the top part of the output plot list are plots showing how the model fits the data In the middle section are the posterior probabilities for the various parameters appearing in the model Finally the bottom contains a number of plots that are meant as aids in understanding the outputs from the simulations Like the Ascii D
87. ing with the maximum deviation being about 10 and a typical deviation being more like one or two The size of the deviations and the presence of a sharp boundary are both data and model dependent However a good rule of thumb concerning the size of these deviations is that each parameter in the model can on average cause a deviation of one and perhaps two e folding and if there are 2 parameters then an average deviation would be 2 to 4 e folding Models with more parameters will deviate from the maximum by roughly the number of parameters times one or two Large deviations caused by a single parameter are hard to obtain simply because such a large deviation in the posterior probability is rejected by the Markov chain THE CLIENT INTERFACE 79 File Package WorkDir Settings Utilities Help Submit Job to Server Server Analysis Option SaveReset RUN Cancel Set Status Set Order 2 ij Find Outliers G Save Get Job Run bmrw200 Include Constant Reset Ascii Data Viewer FID Data Viewer Image Viewer Prior Viewer Fid Model Viewer Plat Results Viewer Text Results Viewer File Viewer Output Plots Log Probability By Repeat Number Data Model and Resid Set1 365 0 sE a oe E Data and Model Set 1 865 5 Residuals Only Set 1 N Rate 1 7866 0 19 Rate 2 366 5 jm Time 1 367 0 XN d IVA Time 2 Amplitude 1 Set REA d Amplitude_2 Set 1 368 0 4 Constant Set 1 368 5 AmpR
88. is a special type of exponential analysis that is very common in NMR In this problem the NMR signal starts at a negative value and decays to a positive value The inversion recover model differs from an exponential plus a constant model only in that the model is typically formulated so that the two amplitudes represent the initial time equal to zero and equilibrium amplitude thus the amplitudes are linear combinations of the amplitudes that would be estimated by an exponential plus a constant model As a side note this package is really a special case of the Enter ASCII package described below We call these special cases preloaded enter ASCII models because the interface preloads the inversion recover model from the system model directory and thus simplifies what the user must do to run this inversion recovery model This package can analyze multiple data jointly to look for a common parameters See Chapter 7 for a description of the inversion recovery package Diffusion Tensor The Diffusion Tensor package analyzes NMR diffusion measurements using one two or three diffusion tensor models with or without a constant These tensor can use either b THE CLIENT INTERFACE eoo File Miel WorkDir Settings Ut Exponential Inversion Recovery Diffusion Tensor Enter Ascii Model Enter Ascii Model Selection Test Ascii Model Magnetization Transfer Magnetization Transfer Kinetics Magnetization Transfer Big Bayes Analyze Bayes Big Peak Little
89. is roughly divided into three groups of plots The first group of plots plot the the data model and residuals in a number of different ways This group plot generally consist of three different plots one of the Data the model and Residuals one plot of the data and the model and finally a plot of just the residuals Figure 3 20 is the result of running a biexponential model with a constant on biexponential data The plot shown in this figure was generated by clicking on the Data Model and Resid Set 1 line in the output plot list This plot contains three traces the data in red the model in blue and the residuals in green These three plots are generated from the Markov chain Monte Carlo simulation that had maximum posterior THE CLIENT INTERFACE 71 Package Bayesian Build Your Own 1D Model WorkDir AbscissaTesting Host radest02bmr702 rad wustl edu File Package WorkDir Settings Utilities Help InvRec f Priors have been saved Submit Job to Seiver Sever Load and Build Model Analysis Options Save Reset RUN j Cancel Set Staus System User Find Outliers Save Getjob Run radest02bmr702 Fuld Save priors Reset Asc Data Viewer FID Data Viewer Image Viewer Prior Viewer Fid Model Viewer Plat Resulis Viewer Text Resuts Viewer File Viewer Fortran C Hodel Viewer Output Prats Prob for DecayRate Given the InvRec Model Date Model and Resid Set 1 f Mean 0 99611 Sd 6 54E 03
90. kDir to a name of your choice Import Working Directories in Batch k reloads a groups of working directories Figure 3 2 When the Files menu is selected this pull down menu is displayed Use this menu to load data download updates to this manual and save and import working directories 3 1 The Global Pull Down Menus The global pull down menus along the top of the start up page are always present on all package interfaces not just the start up page They allow the user to load files select packages configure servers change working directories set options etc Each pull down menu has multiple functions and the following subsections explain these menus in detail and how to go about using them We will take the menu from left to right starting with perhaps the most complicated menu the Files menu 3 1 1 the Files menu The Files menu is a general purpose menu that handle most functions concerning loading images ASCII data and other types of files into the Bayesian Analysis software Figure 3 2 shows what this menu looks like when activated Here is what each selection menu on the Files menu does Load ASCII selection menu loads ASCII data from either an ASCII file or a Bayes Analyze file In either case the data is copied reformatted and saved in the BayesOtherAnalysis directory of the current WorkDir When multiple ASCII files are loaded the currently selected data file is plotted The file format for an ASCII file is package sp
91. l models using Enter ASCII one can then proceed to this package Here one can load up to 10 different models and then use this package to compute the posterior probability for the models The only requirement between the models is that they must process the same data so all models must have the same number of data columns and because ASCII data has the abscissa in the file all models must use the same abscissa See Chapter 22 for a description of the ASCII Model Selection package Test ASCII Model The Test ASCII Model model package supports the other packages that use ASCII Models This package gives one a facility for testing models to ensure they are doing their calculations correctly This package allows load a model and data associated with that model and then the Test ASCII Model package will thoroughly test the model by evaluating the model 10 000 times using parameter sampled from the priors In the process of evaluating the model the package will catch any arithmetic errors that occur and it will show the abscissa value where the invalid arithmetic occurred The outputs form the model include a peak posterior probability estimate of the model and plots of the model signal as a function of the parameter samples and plots of the residuals the difference between the data and the model See Chapter 21 for a description of the test ASCII model package Magnetization Transfer The Magnetization Transfer two sites package solves the Block McConne
92. ll equations to obtain the exchange rate constants for two site magnetization exchange Input to this package is usually the peak amplitudes or intensities from two inversion recovery time courses where the exchanging peaks in are selectively inverted The ASCII file used by this package is three column ASCII one abscissa and the amplitudes of the two exchanging peaks See Chapter 14 for a description of the Magnetization Transfer package Magnetization Transfer Kinetics The Magnetization Transfer Kinetics package is a magnetiza tion transfer package that solves the Block McConnell equations at multiple temperatures and THE CLIENT INTERFACE 39 concentrations to derive the entropy and enthalpies of the the exchange process Input to this package is also three column ASCII with multiple data sets taken at differing temperature and concentrations See Chapter 15 for a description of the Magnetization Transfer Kinetics package Big Magnetization Transfer The Big Magnetization Transfer package solves the magnetization transfer problem when one of the sites can be considered infinite compared to the other See Chapter 13 for a description of the Big Magnetization Transfer package Bayes Analyze The Bayes Analyze package is a time domain frequency estimation package that is fully capable of determining the number of resonances in an fid and estimating the resonance parameters This package can analyze single fid s or it can run multiple fid s and
93. look for frequencies common to these fid s Input to this package can come from different sources and appropriate data conversions are carried out when the data are loaded See Chapter 8 1 for a description of the Bayes Analyze package Big Peak Little Peak The Big Peak Little Peak package analyzes time domain fid data in which there is a single big peak that may be many orders of magnitude larger in intensity the big peak than the metabolic peaks the little peaks of interest The Big Peak Little Peak package solves this problem by treating the big peak as a nuisance and then uses Bayesian probability theory to account for the big peak while simultaneously estimating the frequencies decay rate constants and amplitudes of the resonances of interest See Chapter 9 for a description of the Big Peak Little Peak package Find Resonances The Find Resonances package analyzes NMR fid data looking for resonances The program is a model selection program that is attempting to determine the number of resonances in the data and estimate the parameters associated with those resonances This package uses Markov chain Monte Carlo simulations to determine the posterior probability for the number of resonances in the data This package essentially solves the same problem as the Bayes Analyze package described above However because it uses McMC the calculations are much slower than those in Bayes Analyze but they are much more through often having much better r
94. ly the number of THE CLIENT INTERFACE 43 List of Working Directories test NoSmoothing MEA Working Directory Information and Content This WorkDir bmr 10 jagrp larry Bayes Given Current WorkDir bmr 10 jagrp larry Bayes Given Package BayesExponential Server bayes Server port 8080 Job Status Not Run ASCII data Name D01 dat Type loaded from file Source bmr10 jagrp larry bayesian Bayes test data Exponential ExpOneConstAbs dat Name 002 dat Type loaded from file Source bmrl10 jagrp larry bayesian Bayes test data Exponential ExpThreeNoConstAbs dat Spectral Fid Source bmr10 jagrp larry bayesian Bayes test data BayesAnalyze ethyl ether fid Image data Image bmrl0 jagrp larry Bayes Given images LoadedImage Real 4dfp ifh Source bmrl0 jagrp larry data Tu ForLarry sTest semsdw22 fid Image bmrl0 jagrp larry Bayes Given images LoadedImage Imag 4dfp ifh Source bmrl0 jagrp larry data Tu ForLarry sTest semsdw22 fid Image bmrl0 jagrp larry Bayes Given images LoadedImage Abs 4dfp ifh NETTES Mam LOL er o Ld LT Wo seT Leod lacada Fiel Delete directory Load directory CLOSE J Figure 3 6 When the WorkDir Manager is selected this popup window is displayed Along the left hand side is the list of the working directories By clicking on these working directories the current status of each directory can be viewed and by using the buttons at the bottom working directories can be created loaded or d
95. ms Set 1 369 0 NoiseStdDev Set 1 wu MD Log Likelihood 369 5 Rate_1 vs Rate_2 370 0 Log Probabilit 3 370 5 E 371 0 o a7151 n o 3720 S 372 5 373 04 373 5 374 0 374 5 4 375 5 376 0 376 54 o 377 0 Get MaxEnt Histogram 377 5 lisi View Samples O 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Repeat Number Figure 3 27 When the simulated annealing phase is finished for all of the simulations the program that run the simulations begin gathering samples of each of these simulations The program tries to gather uncorrelated i e independent samples If the user specified 50 simulations and 30 samples the the program tries to gather 30 independent samples of the 50 simulations The shown here is the logarithm of the posterior probability for each simulating plotted by sample number 80 THE CLIENT INTERFACE 3 4 8 Text Results Viewer After an analysis has been run the viewers are used to look at the outputs from the analysis The Text Results view show in Fig 3 28 is a typical example of the Ascii outputs We are going to describe each of these shortly but note that the Text Results Viewer shows the output from two different packages The current package labeled standard and Bayes Analyze The reason the Bayes Analyze package is shown is because that package is unique in that some of the outputs from that package can server as inpu
96. n be used to change the number of data columns Remember if you change the number of data columns the code will need to be modified to accommodate this change Model Vectors can only be changed indirectly This number is a count of the number of parame ters having a parameter type of Amplitude Consequently to change the number of model vectors you must change the number of amplitudes Priors is a display text that indicates the current number of priors To change the number of priors activate the grayed out down arrow on the right side of the prior count label When activated this pull down menu has three options Add New Parameter when activated will popup a window asking you for the name of the new parameter Enter the name of the parameter in the popup and hit OK The parameter will be added to the list of parameters in the model However the prior will be filled in with zero and you must set the prior accordingly To set the prior simply click on the prior name in the list of priors this will display the prior in the area on the top of this window Change the values as you see fit Note the values are updated as you make the changes Remove All will remove all of the priors from this model Note you are not prompted to prevent you from making a mistake the priors are simply removed If this is an error then hit Cancel and Exit to abort your efforts and try again Remove parameter will display a selection list and you may pick
97. n under the Options menu would be very difficult Here we are going to list these options and give some pointers on what they do First the expanded options menu is shown in Fig 3 15 Here is a brief explanation of the various options Data Info Brings up a popup window that displays information about the currently loaded fid This information includes things like the original source fid name The current weighting the units in use the phase the reference and a number of other data items Its basically a dump of all of the relevant parameters concerning this fid Save As Varian fid this functions saves the currently loaded fid as a Varian binary fid file and it does this regardless of the input format of the data So an input data set could have been an Ascii fid and this save command will save the data as a Varian fid Effectively translating the Ascii data to an fid Save As Text Saves the currently loaded fid as a two column Text file Real Imaginary Show Plotted Data brings up the current plot in a popup window that can be viewed printed and saved Clear Data will remove the current fid that is to say the files fid text and procpar will be removed from the current WorkDir fid directory 54 Data Info Save As Varian Fid Save As Text Show Plotted Data Clear Data Apply Phasing set Regions Set Fn Set Lb Set Reference set Units Properties Copy Save as Print Zoom In Zoom Qut Auto Rang
98. nd upper threshold on the pixel values that are displayed To adjust the lower threshold position the cursor on the grayscale bar at the value to be thresholded and do a left mouse click This will move the red hatch mark to the cursor position it will set the minimum threshold and finally it will redisplay the image using this threshold Similarly to set the upper threshold position the cursor on the grayscale bar at the value threshold and do a right mouse click This will move the blue hatch mark to the cursor position it will set the maximum threshold and finally it will redisplay the image using this threshold The threshold hatch marks the blue and red vertical bars can also be dragged That is to say position the cursor on either the red or blue hatch mark and then drag the hatch mark to higher or lower values whichever is appropriate Also the selected thresholds can be moved left or right on the grayscale bar To move the threshold located small tab in the center of the grayscale bar This tab can be dragged left or right to vary the grayscale window that is displayed This tab cannot be dragged until the left or right mouse clicks are used to raise or lower the displayed grayscale 3 4 3 5 the Pixel Info area The Pixel Information area is the area on the top right hand side of the Image Viewer see Fig 3 16 It is used to display information about the image The three widgets contained in this area have the following functions X P
99. ndow For example you might want to specialize a title or some text in the window as a reminder of what you did in the analysis prior to saving the results When activated the check box just to the right will toggle on and off You can also just check the box to enable editing Scroll Up will cause files to be positioned at either the beginning or ending of the file Settings will popup a window that allows you to configure the Text Results Viewer Mostly it allows you to set the fonts and font point sizes The Standard selection list has a number of widgets associated with it and these reports are briefly described here See the individual packages for a more detailed description of these re ports In all cases when a widget in the standard selection list displays a file it is located in your BayesHome CurrentWorkDir BayesOtherAnalysis directory Instructions will redisplay the instructions that are shown whenever a package is started These instructions are typically terse but they will indicate the types of things that must be done to successfully run a package For more information on the individual packages consult the appropriate Chapter THE CLIENT INTERFACE Package Given and Unknown Number of Exponentials WorkDirBayes Host bayes File Package WorkDir Settings Utilities Help Submit Job to Server Server f Analysis Option SaveReset f f f RUN Cancel Save Set Status Order Find Outliers
100. ne 03 is the name of the file being plotted The file is located in the Bayes Home director WorkDir BayesOtherAnalysis directory Line 04 is the title of the plot Line 05 is a long abscissa label Line 06 is a short abscissa label Line 07 is the Y axis label Finally Line 08 on probability plots contains the parameter estimates displayed should the user activate the View Samples button Line 03 is the name of the file being plotted The file is located in the Bayes Home director WorkDir BayesOtherAnalysis directory Line 04 is the title of the plot Line 05 is a long abscissa label Line 06 is a short abscissa label Line 07 is the Y axis label Finally Line 08 on probability plots contains the parameter estimates information displayed as part of the title Show Data From Plot will display the data actually plotted in a popup This display is usu ally two column but it will be multicolumn when plots having more than a single trace are displayed Show Source File for Plot will popup a window containing the original source file This source file can be different from that displayed by the Show Data From Plot widget For example the file containing the data model and residuals is a four column file while a plot of only the data and the model would contain only three columns even though the source file is four columns 3 4 6 1 the Data Model and Residuals Plots It was mentioned early that the output plots list
101. ngle exponential plus a constant so there are three prior probabilities the prior probability for the decay rate constant and the initial and final intensities When an item in list of parameters is activated with a mouse click the prior probability for the selected parameter is displayed in the viewing area and the parameters that describe the prior probability are shown in the entry boxes just above the viewing area The values in the entry boxes can be changed as needed Selecting a different type of prior will cause the entry boxes to change to something appropriate for the selected prior In the example shown the prior is described by three parameters a low a peak and a high The user can set these parameters to any values they wish and the interface will redisplay the prior as to reflect the changes The interface will allows invalid values in these entry boxes for example setting High less than Low but it will not let the analysis to be run with invalid settings If the parameters are invalid and the run button is activated the interface will popup an error message and the error must be corrected before the analysis can be run When an analysis is run a list of the priors selected by the user is sent to the analysis package The package normalizes the priors in such a was as to ensure the prior probability is always between zero and one and then proceeds to use the selected prior in the calculation The normalization for the prior is set discr
102. nimization IEEE Trans on Information Theory IT 27 No 4 pp 472 482 BIBLIOGRAPHY 419 54 Shore J E R W Johnson 1980 Axiomatic derivation of the principle of maximum entropy 55 56 57 58 59 60 and the principle of minimum cross entropy IEEE Trans on Information Theory IT 26 No 1 pp 26 37 Sivia D S and J Skilling 2006 Data Analysis A Bayesian Tutorial Oxford University Press USA Stejskal E O Tanner J E 1965 Spin Diffusion Measurements Spin Echoes in the Presence of a Time Dependent Field Gradient Journal of Chemical Physics 42 1 pp 288 292 Taylor D G Bushell M C 1985 The spatial mapping of translational diffusion coefficients by the NMR imaging technique Physics in Medicine and Biology 30 4 pp 345 349 Tribus M 1969 Rational Descriptions Decisions and Designs Pergamon Press Oxford Woodward P M 1953 Probability and Information Theory with Applications to Radar McGraw Hill N Y Second edition 1987 R E Krieger Pub Co Malabar Florida 1990 Zellner A 1971 An Introduction to Bayesian Inference in Econometrics John Wiley and Sons New York
103. nte Carlo Methods technical report CRG TR 93 1 Dept of Computer Science University of Toronto Neil Jeffrey J and G Larry Bretthorst 1993 On the Use of Bayesian Probability Theory for Analysis of Exponential Decay Data An Example Taken from Intravoxel Incoherent Motion Experiments Magn Reson in Med 29 pp 642 647 Nyquist H 1924 Certain Factors Affecting Telegraph Speed Bell System Technical Jour nal 3 pp 324 346 Nyquist H 1928 Certain Topics in Telegraph Transmission Theory Transactions AIEE 3 p 617 644 Press W H S A Teukolsky W T Vetterling and B P Flannary 1992 Numerical Recipes The Art of Scientific Computing Second Edition Cambridge University Press Cambridge UK Scargle J D 1982 Studies in Astronomical Time Series Analysis II Statistical Aspects of Spectral Analysis of Unevenly Sampled Data Astrophysical Journal 263 pp 835 853 Scargle J D 1989 Studies in Astronomical Time Series Analysis III Fourier Transforms Autocorrelation and Cross correlation Functions of Unevenly Spaced Data Astrophysical Jour nal 343 pp 874 887 Schuster A 1905 The Periodogram and its Optical Analogy Proceedings of the Royal Society of London 77 p 136 140 Shannon C E 1948 A Mathematical Theory of Communication Bell Syst Tech J 27 pp 379 423 Shore J E R W Johnson 1981 Properties of cross entropy mi
104. only updated any when one of the three Submit Job to Server buttons are activated To obtain the current status of a job activate the Get Job button 3 3 The Server area The Server widgets group configures and controls server This widget group is shown in Fig 3 11 In general terms this widget group allows the select and configuration of servers The server widgets group e The server Set button allows the current server to be selected When this button is activated a pull down menu appears containing a list of all of the servers Clicking on a server will cause it to be set as the current server The current server is displayed in the server name text are under this button At the bottom of pull down menu is an item Edit Servers that can be used to modify the list of servers Activating this widget will bring up a popup Chapter 3 1 4 that allows servers to be add deleted and modified as desired This Server Edit popup is also available under the Settings Server Setup menu e The server Status button will send a request for a list of jobs currently running on the server On Linux and Sun systems this request is a simple ps The results of this request are displayed in the Text Viewer at the bottom of the interface e The current Server is displayed in the Server Name text area under the two button in the Server widget group THE CLIENT INTERFACE 49 Server Set will bring up a popup window
105. ord required V Add server J View Server Installation Info J Remove server d Auto Configure Server J OK Figure 3 9 When the Server Setup menu is selected this popup is displayed It allows Servers to be add remove and change McMC repetitions can be set and thus the number or samples gathered for use in computing mean and standard deviations parameter estimates The number of samples number of repeats times number of simulations Finally the minimum number of annealing steps to take during the the simulated annealing phase can be set For more on how the McMC simulations are run see Section B the Server Setup submenu Activating the Settings Server Setup menu will bring up the popup shown in Fig 3 9 The Settings Server Setup menu is a popup that allows servers to be add delete and modify To select a server simply click on the server name After selecting a server that server becomes the current server and any job submitted will be sent to the selected server Note that servers can also be selected by activating Server Set button on all package interfaces When servers are selected on the Settings Server Setup popup the server name port Bayes user account etc are displayed Any field except the server name and port number can be modified However modifying anything other then the user name and email preferences is not advised Indeed modifying the processing account password settings or queue name will l
106. os is the pixel number in the X horizontal direction The first number is the pixel number in the raw image Note that the graphic display in the Image Viewer is a 512 x 512 pixel display The second number the one in parentheses is the pixel number in the graphics area and ranges from 0 to 511 Y Pos is the pixel number in the Y vertical direction Value is the intensity of the pixel from the raw image at the current cursor position 3 4 3 6 the Image Statistics area is located on the right at the bottom of the Image Viewer These widgets remain empty until one hits the Get Statistics button When this button is activated the interface will compute a few basic statistics about the ROI if present and about the entire image if no ROI is present Here is a brief description of the information displayed in these widgets Mean contains the mean value of the images pixels in the selected region Max contains the maximum value of the image pixels in the selected region Min contains the minimum value of the image pixels in the selected region Sdev contains the standard deviation of the selected region If p stands for the th pixel in the selected ROI containing N pixels then the Sdev value is calculated as N 1 2 Sdev Y pi Mean 3 1 e ROI THE CLIENT INTERFACE 61 and Mean is the mean pixel value in the ROI and is given by 1 N Mean x S pi 3 2 ic ROI Note for absolute value images this cal
107. ot In release 4 10 a new type of plot was added see Fig 3 23 For each plot of the posterior probability for a parameter there is an addition scatter plot of the parameter verses the posterior probability If the posterior probability for a given parameter is highly symmetric having a well defined maximum then this new plot Fig 3 23 will look almost exactly like the plot shown in Fig 3 22 In this new plot the horizontal axis is the value of the parameter and the vertical axis is the unnormalized poste rior probability When the Markov chain Monte Carlo simulations are running it is the logarithm of the posterior probability that is computed To obtain the unnormalized posterior probability shown in this plot we locate the sample that has maximum posterior probability subtract that value from all of the other samples and then exponentate Finally the samples are normalized so that the peak sample is the same as the peak shown in Figure 3 22 When the posterior probability is well peaked these plot is almost identical to the plot shown in Fig 3 22 One of the reasons this plot was added was to help eliminate a common confusion In the heading of the plots of the posterior probability part of that heading reads Parameter Value From Max Prob Sim xxxx where Parameter Value is the name of the parameter being shown for example in the exponential package it would read Rate 1 and xxxx is the value of the parameter
108. place the cursor where the ROL is to start and click the left mouse button A dot should appear at this vertex Now move the cursor to the place where Move to the next polygon vertex to be and click the left mouse button Continue this for as long as needed However to close and end drawing the ROI end the drawing by placing the cursor on the starting vertex and left mouse click a second time 2 when activated this button will expand a square ROI This button only functions when a square ROI is present ms when activated the image is flipped left to right 1 when activated the image is flipped top to bottom file and the Ascii file viewer is activated displaying the extracted pixels This widget only functions when an ROI is present e when activated the interface will attempt to determine a gray scale appropriate for the image stack When the calculation is completed the images are displayed using the new gray scale lt when activated the original image is displayed using the original gray scale B when activated the image stack is copied and exported to ImageJ gt when activated the user can set user preferences This is the same popup that is available on the Settings Preferences menu 60 THE CLIENT INTERFACE 3 4 3 4 the Grayscale area on the bottom The area at the bottom of the Image Viewing area is a grayscale area that can be used to manually set the grayscale Here setting the grayscale means setting a lower a
109. rain assigned By selecting one of menu items the interface s will join that working directory and if an analysis is MultipleSclerosis present it will restore that analysis to its previous sta NonlinearBayesianPhasing tus Edit Figure 3 5 When the WorkDir menu is selected this pull down menu is displayed It contains a list of all of the current Working directories When a working directory is selected the interface will save the status of the current WorkDir and then change into the selected working directory and restore that working directory to its previous status The last entry on this menu is the Edit button When activated the edit button will bring up the popup shown in Fig 3 6 that allows one to modify and manage working directories Along the left hand side of this menu is a list of all of the working directories As noted these are the names of the working directories as defined by the user By clicking on these items the status of the working directory is displayed Status information includes the package that is loaded whether or not the package has been run and information about the files ASCII fid and Images that have been loaded Additionally information about the server that is selected in this WorkDir is displayed Finally using the buttons along the button of the WorkDir manager a new WorkDir can be created To create a WorkDir simply enter the name of the directory in the text area in front of the New
110. rameter increases The lower part of the Bayes accepted file is package specific and the number of entries in this part of the report can be highly variable In general terms the lower part of the report will THE CLIENT INTERFACE 83 contain some statistics about how often each parameter in the Markov chain Monte Carlo simulation is being accepted and rejected Here is an example taken from the Enter Ascii Model package with the marginalized two exponential plus a constant model Param Desc Avg Param Param Sd Proposal Prior Contrib Rate DecayRatel 2 682716E 01 2 179858E 02 4 367748E 02 4 525808E 00 0 2393 DecayRate2 9 382104E 01 4 349060E 02 7 788657E 02 3 835734E 00 0 2485 Because this is a marginal probability density function only the decay rates are varied in the McMC simulations and consequently only the decay rates are shown in the accepted report The entries are the average parameter value its current standard deviation the current proposal used in the McMC simulation the contribution of this parameter to the logarithm of the prior probability and finally the acceptance rate The acceptance rate labeled Rate is the number of times a parameter was accepted divided by the total number of times a new value was proposed The packages try to keep this acceptance rate between 20 and 30 For more on how this is done see Section B and for more about the Bayes accepted report generated by a specific package consult the appropriate Chapter
111. ry usage If 1GB of memory is not enough it is possible to get 2GB of memory However the launch jnlp files on the server must be modified to do this If assistance is needed in modifying these files please contact System Info will display information about the current installation on the client machine This information could be important to us when trying to help diagnosis problems The displayed information includes the user name the user home directory the architecture OS Os version file separator and the version of Java in use In case of problems all of this information could be useful in figuring out what is going on THE CLIENT INTERFACE 47 Software Update will bring up a popup showing all of the servers currently have defined and it will indicate if each server has the most recent version of the software installed on it So the Software Update utility check with us here at Washington University to find out what the current version of the software is and it then checks each of the servers to see if they are up to date If the software is not up to date log into each out of date server as the bayes user and then update i e reinstall the software 3 1 6 the Help menu The Help menu not shown will provide help concerning the current release of the software There are four different types of help available Release Notes will activate a web browser and download a page that describes the changes in the current version of the Ba
112. s Prior Type is a pull down menu that allows you to select the prior type Edit type sets whether or not the prior type can be edited by the user The default allows the field to be edited Order indicates if this parameter must be ordered or not The default is not to order the parameters If the parameters are to be ordered they can be ordered from low to high or high to low Edit order indicates if the order parameter can be modified or not Usually when a param eter is ordered this cannot be safely change Safely change in the sense that the model will continue to work correctly Consequently we default this to not editable but allow the user to change this field at his own peril Non Linear is the default parameter type this selection menu can be used to set the param eter to amplitude or parameter Compile Results will redisplay the results from the previous compile Bibliography 1 Bayes Rev T 1763 An Essay Toward Solving a Problem in the Doctrine of Chances Philos Trans R Soc London 53 pp 370 418 reprinted in Biometrika 45 pp 293 315 1958 and Facsimiles of Two Papers by Bayes with commentary by W Edwards Deming New York Hafner 1963 Bretthorst G Larry 1988 Bayesian Spectrum Analysis and Parameter Estimation in Lecture Notes in Statistics 48 J Berger S Fienberg J Gani K Krickenberg and B Singer eds Springer Verlag New York New York Bretthorst G Larr
113. s For example the Ascii Model Selection program can load up to 10 models The prior probability for the model is uniform i e one over the number of models Gaussian selects a Gaussian prior probability having the mean and standard deviations set by the user Gaussian prior probabilities are the most common prior probability used in the software Its a natural prior for amplitudes and it is typically used for any other parameter that can take on both positive and negative values Exponential selects a exponential prior probability having the decay rate constant set by the user Exponential priors are typically used in the Bayesian Analysis software for discrete parameters For example the prior probability for the number of sinusoids in a model would typically be assigned a exponential prior Positive selects a positive prior probability having a peak value set by the user An example of this prior is shown in Fig 3 18 This prior is meant for scale parameters and scale parameters can t be negative and this prior will not allow parameters to go to zero let alone negative This is clearly illustrated in Fig 3 18 because the probability goes to zero as the value of the parameter goes to zero This priors behavior is asymptotically Jeffreys 32 again a characteristic desirable for scale parameters This is also illustrated in Fig 3 18 because for large parameter the prior is dropping off very slowly indeed like 1 X Finally given that
114. s are analyzed jointly looking for common frequencies with fid dependent amplitudes The amplitudes are combined with the arrayed variable from the procpar in the fid subdirectory in the current WorkDir Load Spectroscopic fid loads time domain spectroscopic fid data from several sources Varian fid data Siemens rda Siemens Raw data and ASCII Text fid data When any of these selection menus are activated they brings up a popup that allows navigation to the appropriate file and then load it When data are loaded the data are copied to the fid Subdirectory of the current WorkDir and a Varian fid procpar and text file are written into this Subdirectory If the loaded fid is a Varian fid the procpar is copied from the source directory otherwise a procpar is generated and modified to reflect the number of data values acquisition time and sweep width of the current data The data are then Fourier transformed and the real part of the discrete Fourier transform is displayed using the phasing parameters in the procpar Load Image menu handles the task of loading various kinds of image data into the Bayesian Analysis package The menu will loads both k space and image data The first two selection menus items will read k space data and then convert the k space data into images The remaining menu items all read various types of images and convert them into our internal format Images are stored in the Images Subdirectory of the current
115. s exponential analysis with one or more exponentials with or without a constant diffusion tensor Addition ally the users can copy and the edit an example model to create models of his own These models can be loaded from the users home directory and then used to analyze the image The Image Pixels package includes an option for finding the peak of the posterior probability When this option is selected a different program is actually run by the package This program is a searching algorithm that looks for the peak in the posterior probability for the parameters in the model These peak parameter estimates are then used to generate maps of the various parameters appearing in the model Because this program is a searching routine rather than an McMC routine it is very fast and can give good results using any ASCII model in a fraction of the time needed to run the Markov chain Monte Carlo simulations See Chapter 28 for a description of the Image Pixel package Image Pixel Model Selection The Image Pixels Model Selection package extends the concepts in Analyze Image Pixels to model selection In this package one can load a number of different models and then use Bayesian probability theory to determine which model best accounts for the data The models in use here are the same models mentioned in both Analyze Image Pixels and the Enter ASCII packages However here because the models can have different param eterizations the output images are constr
116. so 13 bins are included and the value of the Gaussian is added to the histogram Finally the histogram is normalized so that the sum over all bins is one This rather crude histogram technique works well provided the histograms are reasonably smooth One can replace a smoothed binned histogram by a fully Bayesian estimation of that histogram This MaxEnt histogram is obtained by activating the Get MaxEnt Histogram button near the bottom of the output plot list Activating this button will send a request to the selected server to run the MaxEnt Histogram package The interface runs the request in background so continue working on the interface If the same smoothed histogram is being displayed when the MaxEnt histogram package finishes the smoothed binned histogram is replaced by the MaxEnt histogram and the histogram is redisplayed If a different smoothed histogram is displayed the MaxEnt histogram overwrites the appropriate smoothed histogram and the MaxEnt histogram will be displayed the next time the user displays the histogram The MaxEnt calculation is as computationally intensive as running many other package so only generate a MaxEnt histogram when a better characterization of the samples is really needed Because this calculation is a full Bayesian calculation the resulting histograms have error bars For a detailed description of these Bayesian calculations see Chapter 3 4 7 the Posterior Probability Vs Parameter Samples pl
117. st a data point number and column two is a sample from the unknown density function The program models the density function as a Maximum Entropy moment distribution having an unknown number of Lagrange multipliers So the parameters are Lagrange multipliers and the unknown number of them The program does a Markov chain Monte Carlo simulation with simulated annealing where the number of multipliers is one more parameter in the simulation Outputs include the posterior probability for the number of multipliers the posterior probabilities for the multipliers scatter plots and the polynomials used in the calculations See Chapter for a description of the Maximum Entropy Histograms package Binned Histograms The Binned Histogram package is a new histogram package In the previous release of the software there was a MaxEnt histogram package that infers histograms that are functionally Maximum Entropy moment distributions As such the program is inferring the moments and the number of moments needed to represent the input samples from unknown density This procedure works well for compact distribution but fails badly when the dis tribution of samples is multimodal In order to estimate density functions when the samples are multimodal we added a histogram package that infers what can only be called binned his tograms These histograms can represent any distribution they have error bars on the number of counts in the bins and the user can indicate if t
118. t color than the black of the viewing area This area can be used to adjust the position of the display vertically So if the base line of the spectrum is too high or too low place the cursor in this shaded region and then hold down the center mouse button and the display can be moved up or down The type of display can be changed on the Fid Data Viewer The top center pull down menu that usually reads SPECTRUM REAL can be used to change the type of display When this pull down menu is extended the menu shown in Fig 3 14 is displayed Most of the options are self explanatory and we give no further explanations of this viewer here except to note that all of the cursor and mouse functions work on the different data types 52 THE CLIENT INTERFACE Given and Unknown Number of Exponentials test2 Host bayes File Package WorkDir Settings Utilities Help Submit Job to Server Server Model Analysis Option SaveReset RUN Cancel Set Status Set Order X Find Outliers O Save Get Job Not Run bmrw208 Include Constant Q Reset Ascii Data Viewer FID Data Viewer Image Viewer I Prior Viewer I Fid Model Viewer Plot Results Viewer Text Results Viewer File Viewer Trace MIS SPECTRUM REAL M Cursor A Cursor B O J x aj Figure 3 13 The Fid Data Viewer is used to display fid files When activated the spectrum of the currently loaded fid is displayed If no fid data are loaded an empty viewer is displ
119. te Carlo to ap proximate the Bayesian posterior probability for the parameters appearing in the model To do this a Markov chain Monte Carlo simulation is used to draw samples from the joint posterior probability for all of the parameters appearing in the model and Monte Carlo integration is used to obtain samples from the posterior probabilities for the individual parameters We display these samples in several different ways This default view of these samples is as a smoothed binned histogram like the one shown in Fig 3 22 This particular plot is for the posterior probability for the smallest decay rate constant in a biexponential model containing a constant However the samples themselves can be viewed by activating the View Samples button at the bottom of the output plot list area The default binned histograms are generated vary crudely and are only meant as an aid in understanding things like the mean standard deviation and symmetries of the samples they are not used for any calculations Indeed in the output reports all parameter estimates means peaks 72 THE CLIENT INTERFACE and standard deviations are computed directly from the samples To generate these smoothed binned histograms a Gaussian is placed in the histogram at the point where a sample occurred This Gaussian has a standard deviation such that it goes through one e folding every two bins in the histogram The Gaussian is then evaluated over a symmetric 6 bin interval
120. the probability gain and the date and time the model was added For a complete description of this file see Subsection 8 5 3 Bayes params The bayes params file is written by the interface and serves as the input parameter file to Bayes Analyze It contains various parameter settings and the initial model to be processed The parameter file is divided into three general sections a header the global parameters and the resonance parameters Each of these three sections is describe in detail in Subsections 8 3 8 5 1 2 and 8 5 1 3 Console log is a running history of what model is being analyzed at the current time Here is a small snippet of this file bayes_analyze VO1 20 00 Developed by Washington University School of Chemistry and Monsanto St Louis NMR Center Base 10 Log Evidence for The First Resonance is 268 3 Beginning a 1 resonance model Base 10 Log Of The Probability for 1 Resonance 3 75974811E 03 Base 10 Log Evidence for The Next Resonance is 59 2 Beginning a 2 resonance model Base 10 Log Of The Probability for 2 Resonances 3 71837136E 03 Base 10 Log Evidence for The Next Resonance is 65 6 As you can see from the above list the console log is just an indication of the current model the logarithm of the posterior probability for that model and finally the log of the evidence that there is another resonance in the data log is a complete list of all of the steps taken in the Levenberg Marquardt searching algorithm
121. the selected data set is 50 THE CLIENT INTERFACE Bayesian Build Your Own 1DModel test2 Host bayes File Package WorkDir Settings Utilities Help Submit Job to Server Server Load and Build Model Analysis Options SaveReset RUN Cancel Find Outliers 3 p Get Job Not Run Rest Const f Loaded Not Built _ Ascii Data Viewer FID Data Viewer li Image Viewer Prior Viewer Fid Model Viewer Plot Results Viewer Text Results Viewer File Viewer Fortran C Model Viewer Ascii Data 001 dat 200 002 dat ioo 003 dat 004 dat 180 170 160 NUN 120 110 g01 1 g e y RR J Fs Figure 3 12 The Ascii Data Viewer is used to display Ascii files Change files by clicking on the name of the file to be viewed The Delete button will delete the selected file and the italics 7 button in the circle will display everything known about the file This button is redundant with a right mouse and selecting show info THE CLIENT INTERFACE 51 plotted on the right hand side viewer If the data are multicolumn data for example complex data the plot will have multiple traces on it This viewer responds to a right mouse click in both parts of the viewer In the file list area the left hand side the right mouse click shows a submenu that allows file deletion displays information about the selected
122. tion about the currently loaded fid is requested The Fid Data Viewer uses left right and center mouse clicks The left and right mouse clicks are used to set the locations of a left and right cursor These cursors are displayed in Fig 3 13 as the two vertical red lines When set the frequencies of these cursors are shown in in at the bottom of the viewer as Cursor A the left cursor and Cursor B the right cursor The difference between these cursors is shown in the Delta display Note the units used in these three display areas are the same as the units on the displayed frequency axis When the left and right cursors are displayed the Expand button can be used to expand the selected area The Full button will display the full spectrum and the Clear Cursors will remove the cursors from the display The vertical scale on the display can be adjusted automatically using the Autoscale button or it can be adjusted manually The center mouse button is used to adjust the vertical scale manually If cursor is placed anywhere in spectrum display above the axis and hit the center mouse button the display vertical scale is adjusted upward If cursor is placed below the axis and hit the center mouse button the vertical scale is reduced In addition to adjusting the vertical scale the position of the spectrum in the viewer can be changed The left hand part of this viewer has a vertical strip that is shaded a slightly differen
123. ts to the current Ascii package Consequently the current working directory can contain outputs from the current package in BayesOtherAnalysis and outputs from Bayes Analyze in BayesAnalyzeFiles Activating any of the items on these selection menus will cause the appropriate file from the selected package to be listed in the Viewing area If the requested file does not exists then an appropriate message is displayed You can also switch reports by selecting them or by using the up and down arrows on your keyboard However you cannot jump between the standard output and the Bayes Analyze outputs using the up and down arrows The entries in both text results viewers standard and Bayes Analyze are fixed and do not vary from package to package Along the top of the viewing area are a number of buttons that are specific to the Text Results Viewer Here is a description of these buttons Print will direct the currently selected file to the printer the button will popup a widget that allows you to select a few print options including the printer Copy will copy the currently selected file to your clipboard Save will save the current copy of the file on top of the original file located in BayesHome Current WorkDir BayesAnalyzeFiles Save As will popup a navigation window that will allow you to navigate to the location you wish the file to be saved and then it will save the file Enable Editing will allow you to change the contents of the viewing wi
124. tter plot is elongated along the vector sum of the decay rate constants and it is contracted by about a factor of 3 along the vector difference This implies that the sum of the decay rate constants is not well determined compared to the difference This type of correlation is very common among models containing multiple exponentials Not all packages produce scatter plots and even packages that do generate scatter plots do not always generate scatter plots of all of the parameters For example here there are three amplitudes and two decay rate constants in the model but only a scatter plot of the decay rate constants was output That s because the exponential package uses a marginal posterior probability and the amplitudes are not varied by the Markov chain Monte Carlo simulations Scatter plots are only produced for parameters that are varied by the simulations Additionally some packages have a very large number of parameters and because the number of scatter plots increases like the square of the number of parameters scatter plots are typically not output when the number of these plots would be very large 3 4 7 3 the Log Probability Plot The last plot that we are going to discuss is shown in Fig 3 27 This plot is a bit of a mess and generally speaking the messier it is the better In the Markov chain Monte Carlo simulations used by the Bayesian Analysis software multiple chains are run in parallel In the annealing phase the simulations
125. ucted from the derived parameters See Chapter 29 for a description of the Image Pixel Model Selection package 3 1 3 the WorkDir menu Working directories are directories that are used to run configure and store analysis in the Bayesian Analysis Software package They are physically located in the current Bayes Home directory The default location of the Bayes Home directory is the user home directory and the default name of the Bayes Home directory is Bayes The name and location of the Bayes Home directory can be configured using the Settings preferences popup and multiple Home directories are allowed The working directory menu called WorkDir is generated on the fly and contains a list of the working directories in the current Bayes Home directory Additionally the WorkDir menu contains one fixed menu item named Edit The WorkDir menu is a pull down menu that allows the user to manage working directories Fig 3 1 3 The top part of this menu will list all of the working directories in the current Bayes Home directory The name of the working directories are assigned by the user and the name can be descriptive of the type of analysis being done in that directory For example in Fig 3 1 3 all of the working directories have names that indicate of project the user was working on 42 THE CLIENT INTERFACE Ba Anal The contents of this menu varies depending on the ayesAnalyze number of working directories and the names that have MouseB
126. um to one However the Prior Viewer does not normalize these priors rather the viewer sets the largest value in the prior to one So care must be taken when comparing one prior to another because the prior scales shown in the viewer are not the same as those used in the calculation 3 4 5 fid Model Viewer Free induction decay data are time domain data However most people look at fid data in the frequency domain This presents a unique problem for frequency finding packages because they work in the time domain but their outputs will almost certainly be viewed in the frequency domain The frequency finding packages either generate time domain models of the fid data directly or they generate a series of Ascii Model Files that can be used to generate a time domain fid model of the data Either way the Fid Model Viewer must sometimes generate a time domain fid model and then convert the time domain fid model in the frequency domain for viewing The Fid Model Viewer shown in Fig 3 19 is used to display the results from the analysis of an time domain fid in the frequency domain This viewer is activated when the Fid Model Viewer button is activated If a time domain model exists in the package it is Fourier transformed phased and the absorption mode spectrum is displayed If no time domain model exists rather if Ascii Model Files exist then the user must generate a time domain fid model using the Build BA Model For fid button When activated
127. will be checked Multiple images can be selected either one at a time or in blocks To select a single image use the control left mouse click and the image will be selected Multiple images can be selected by first selecting a single image and then using a shift left mouse click on another image to select all images between the first and second selected image Clicking on a single image will deselect all but the single image clicked on Selected images are used in some of the packages to indicate which images are to be processed by a package The Image List and Image Viewing areas responds to a right mouse click When activated a menu of options appears this menu is shown in Fig 3 17 Here is a list of these menu options and the function they perform Display Full Image will zoom the display out to show the full image Delete Selected will delete the currently displayed image Delete All will delete the all images contained in the image Subdirectory Autoset Grayscale For Entire Stack will attempt to set a grayscale that can be used do display all images Autoset Grayscale For Current Image will attempt to set a grayscale that can be used do display the current images View Selected Pixels as Text will display the pixel values contained in an ROI in a popup text window Load Selected Pixels will load the pixel values contained in an ROI as an Ascii data set The abscissa values in this data set are pixel numbers Loading pixel values will fail
128. y 1990 An Introduction to Parameter Estimation Using Bayesian Prob ability Theory in Maximum Entropy and Bayesian Methods Dartmouth College 1989 P Foug re ed Kluwer Academic Publishers Dordrecht the Netherlands pp 53 79 Bretthorst G Larry 1990 Bayesian Analysis I Parameter Estimation Using Quadrature NMR Models J Magn Reson 88 pp 533 551 Bretthorst G Larry 1990 Bayesian Analysis II Signal Detection And Model Selection J Magn Reson 88 pp 552 570 Bretthorst G Larry 1990 Bayesian Analysis III Examples Relevant to NMR J Magn Reson 88 pp 571 595 Bretthorst G Larry 1991 Bayesian Analysis IV Noise and Computing Time Considera tions J Magn Reson 93 pp 369 394 Bretthorst G Larry 1992 Bayesian Analysis V Amplitude Estimation for Multiple Well Separated Sinusoids J Magn Reson 98 pp 501 523 Bretthorst G Larry 1992 Estimating The Ratio Of Two Amplitudes In Nuclear Magnetic Resonance Data in Mazimum Entropy and Bayesian Methods C R Smith et al eds pp 67 77 Kluwer Academic Publishers the Netherlands Bretthorst G Larry 1993 On The Difference In Means in Physics amp Probability Essays in honor of Edwin T Jaynes W T Grandy and P W Milonni eds pp 177 194 Cambridge University Press England Bretthorst G Larry 1996 An Introduction To Model Selection Using Bayesian Probability Theory
129. y Theory 2o k ko xo dee eee x 4 4 a X m RO Ee 91 42 Assigning Probabilities 2 666444 cee coo a br ee a 94 4 3 Example Parameter Estimation e e a 101 43 1 Define The Problem 2 0 aaa x99 ea XR 102 4 3 1 1 The Discrete Fourier Transform lt ss sec o o 102 43012 JAMBES Dc a o e E dh 105 4 3 2 State The Model Single Frequency Estimation 106 430 Apply Probability Theory 20399 39 9 3 oy a 107 ASA Assign The Probabilities 65 323293 ee oko ko E Ro EEG XXE be ees 110 4 3 5 Evaluate The Sums and Integrals elles 112 4 3 6 How Probability Generalizes The Discrete Fourier Transform 115 LOL PORN 50x 0x Eee S lh ADAC Stee e QE e ep ag ul ie Se eem 118 4 9 8 Parameter Estimates 29 00885024 koc x 93 3 99 9 d ege qn 124 44 Summary and Conclusions aaa da a o eoe HA RR ee aa 127 Given Exponential Model 129 DL The Bayesian Calculation oes wo m 9 x ee RE A EE 131 5 2 Outputs From The Given Exponential Package 133 Unknown Number of Exponentials 135 6 1 The Bayesian CAIGDBUIORS oscar 4 4 6 Od Roe Rome ee ETE RC RU 137 6 2 Outputs From The Unknown Number of Exponentials Package 140 Inversion Recovery 143 Til The Bayesian Calculation 6 a mox c x RA X X ED OR O3 RF RR A 145 7 2 Outputs From The Inversion Recovery Package 146 Bayes Analyze 147 Ol Bayes Model 03 6 s eet tPA ee EUR bee beet REESE OOS 151
130. y being displayed This is done by simply moving either the slice or element number slider to the desired image Alternately the slice or element number can be entered and the viewer will display the desired image 3 4 3 3 the Image Viewing area The area in the center of the Image Viewer is used to display images The Image Viewing area responds to a right mouse click and the widgets on this submenu are the same as those shown in THE CLIENT INTERFACE 59 Fig 3 17 and we urge people to read the previous Subsection to determine their function However the image Viewing area has two menus that can be used to manipulate images The first of these menus is at the top of the image viewing area Here is a close up of this menu Each of the buttons on 0 1M8U 4 this menu performs various tasks associated with images When activated clicked on the functions of these buttons are L when activated a square ROI can be drawn on the image Put the cursor in the image where an ROI is desired Hold down the left mouse and drag the cursor diagonally to draw the ROI When an ROI is present the buttons on the right hand side of the Image Viewer can be used to compute some statistics about values of the pixels We will have more to say about this in Section 3 4 3 6 2d the star will create a point ROI Simply place the cursor on the pixel to be capture and click the left mouse button when activated the polygon widget draws a polygon ROI To do this
131. yesian Analysis Software Those release notes contain links to the main BayesianAnalysis home page and a chain of links that will describe in the previous releases Online Manual will download the current version of the manual and the display that manual in the Acrobat reader Bayes Analysis Home Page will load the home page from the BayesianAnalysis wustl edu web site and bring that page up in the default web browser That page contains a description of the software as well as the release notes for the current and previous versions of the software Contact Us bring up an email client with my email address in it so that questions can be directly addressed to me 3 2 The Submit Job To Server area Just below the global pull down menus there are a number of widget groups that are used to configure a package These widget groups are different for different packages And details on a package specific widget group consult the chapter on that package However their are two widget groups that are global in the sense that they occur on all packages In the next two Subsections we are going to describe these widget groups and their function The first of these widget groups is called the Submit Job To Server widget group and this widget group is shown in Fig 3 10 Below the global menus is an area that is used to configure a package Run will first check to see if all the required elements are set for this particular job If everything is prop

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