Package `coda`
Contents
1. Usage autocorr plot x lag max auto layout TRUE ask Arguments x A Markov Chain lag max Maximum value at which to calculate acf auto layout If TRUE then set up own layout for plots otherwise use existing one ask If TRUE then prompt user before displaying each page of plots Default is dev interactive in R and interactive in S PLUS graphical parameters See Also autocorr batchSE Batch Standard Error Description Effective standard deviation of population to produce the correct standard errors Usage batchSE x batchSize 100 6 bugs2jags Arguments x An mcmc or memc list object batchSize Number of observations to include in each batch Details Because of the autocorrelation the usual method of taking var x n overstates the precision of the estimate This method works around the problem by looking at the means of batches of the parameter If the batch size is large enough the batch means should be approximately uncorrelated and the normal formula for computing the standard error should work The batch standard error procedure is usually thought to be not as accurate as the time series meth ods used in summary and effectiveSize It is included here for completeness Value A vector giving the standard error for each column of x Author s Russell Almond References Roberts GO 1996 Markov chain concepts related to sampling algorithms in Gilks WR Richard son S and Spiegelhalter DJ Mark2. Description The potential scale reduction factor is calculated for each variable in x together with upper and lower confidence limits Approximate convergence is diagnosed when the upper limit is close to 1 For multivariate chains a multivariate value is calculated that bounds above the potential scale reduction factor for any linear combination of the possibly transformed variables The confidence limits are based on the assumption that the stationary distribution of the variable under examination is normal Hence the transform parameter may be used to improve the normal approximation Usage gelman diag x confidence 0 95 transform FALSE autoburnin TRUE multivariate TRUE Arguments x An mcmc list object with more than one chain and with starting values that are overdispersed with respect to the posterior distribution confidence the coverage probability of the confidence interval for the potential scale reduc tion factor transform a logical flag indicating whether variables in x should be transformed to im prove the normality of the distribution If set to TRUE a log transform or logit transform as appropriate will be applied 14 gelman diag autoburnin a logical flag indicating whether only the second half of the series should be used in the computation If set to TRUE default and start x is less than end x 2 then start of series will be adjusted so that only second half of series is used multi
3. read and check Read data interactively and check that it satisfies conditions Description Input is read interactively and checked against conditions specified by the arguments what lower upper and answer in If the input does not satisfy all the conditions an appropriate error message is produced and the user is prompted to provide input This process is repeated until a valid input value is entered Usage read and check message what numeric lower upper answer in default Arguments message message displayed before prompting for user input what the type of what gives the type of data to be read lower lower limit of input for numeric input only 30 read coda upper upper limit of input for numeric input only answer in the input must correspond to one of the elements of the vector answer in if supplied default value assumed if user enters a blank line Value The value of the valid input When the default argument is specified a blank line is accepted as valid input and in this case read and check returns the value of default Note Since the function does not return a value until it receives valid input it extensively checks the conditions for consistency before prompting the user for input Inconsistent conditions will cause an error Author s Martyn Plummer read coda Read output files in CODA format Description read coda reads Markov Chain Monte Carlo output in the CODA format produ
4. Martyn Plummer References Spiegelhalter DJ Thomas A Best NG and Lunn D 2004 WinBUGS User Manual Version 2 0 June 2004 MRC Biostatistics Unit Cambridge See Also read coda rejectionRate 33 rejectionRate Rejection Rate for Metropolis Hastings chains Description rejectionRate calculates the fraction of time that a Metropolis Hastings type chain rejected a proposed move The rejection rate is calculates separately for each variable in the mcmc obj argu ment irregardless of whether the variables were drawn separately or in a block In the latter case the values returned should be the same Usage rejectionRate x Arguments x An mcmc or mcmc list object Details For the purposes of this function a rejection has occurred if the value of the time series is the same at two successive time points This test is done naively using and may produce problems due to rounding error Value A vector containing the rejection rates one for each variable Author s Russell Almond spectrumo Estimate spectral density at zero Description The spectral density at frequency zero is estimated by fitting a glm to the low frequency end of the periodogram spectrum0 x length x estimates the variance of mean x Usage spectrum0 x max freq 0 5 order 1 max length 200 34 spectrumO Arguments x A time series max freq The glm is fitted on the frequency range 0 max freq order Order
5. a vector or matrix of MCMC output the iteration number of the first observation the iteration number of the last observation the thinning interval between consecutive observations An object that may be coerced to an memc object Further arguments to be passed to specific methods The format of the memc class has changed between coda version 0 3 and 0 4 Older memc objects will now cause is mcmc to fail with an appropriate warning message Obsolete mcmc objects can be upgraded with the mcmcUpgrade function Author s Martyn Plummer See Also mcmc list memcUpgrade thin window mcmc summary mcmc plot mcmc mcmc convert Conversions of MCMC objects Description These are methods for the generic functions as matrix as array and as mcmc as matrix strips the MCMC attributes from an mcmc object and returns a matrix If iters TRUE then a column is added with the iteration number For mcmc list objects the rows of multiple chains are concatenated and if chains TRUE a column is added with the chain number mcmc list objects can be coerced to 3 dimensional arrays with the as array function An memc list object with a single chain can be coerced to an memc object with as mcmc If the argument has multiple chains this causes an error Usage S3 method for class mcmc as matrix x iters FALSE S3 method for class mcmc list as matrix x iters FALSE chains FALSE S3 met
6. e 4 om eR OR R Eom A Ry E e 36 li e ee BG Be Sw we ee Sh e By Se Se Ae Be ee a 36 time mcm eai e eru Se AS Bae Bed bk E See dome ee 37 traceplot s e c los bo SLE ORAS eee EGR oS Reb dee Eo oe oe 38 trellisplots amp 2x ute s E x RA ooh os EE ESSE See eee es 38 Varnames vede Sue ae Reo ose eee aw ARIS a d ML EU E 42 is ANN 43 44 as ts mcmc 3 as ts mcmc Coerce mcmc object to time series Description the as ts method for mcmc objects coerces an mcmc object to a time series Usage S3 method for class mcmc as ts x Arguments x an mcmc object unused arguments for compatibility with generic as ts Author s Martyn Plummer See Also as ts autocorr Autocorrelation function for Markov chains Description autocorr calculates the autocorrelation function for the Markov chain memc obj at the lags given by lags The lag values are taken to be relative to the thinning interval if relative TRUE High autocorrelations within chains indicate slow mixing and usually slow convergence It may be useful to thin out a chain with high autocorrelations before calculating summary statistics a thinned chain may contain most of the information but take up less space in memory Re running the MCMC sampler with a different parameterization may help to reduce autocorrelation Usage autocorr x lags c 0 1 5 10 50 relative TRUE 4 autocorr diag Arguments x an memc object lags a vector of lags at
7. the second after discarding the first segment the third after discarding the first two segments and so on The last Z score is calculated using only the samples in the second half of the chain Usage geweke plot x fracl 0 1 frac2 0 5 nbins 20 pvalue 0 05 auto layout TRUE ask Arguments x an mcmc object frac1 fraction to use from beginning of chain frac2 fraction to use from end of chain nbins Number of segments pvalue p value used to plot confidence limits for the null hypothesis auto layout If TRUE then set up own layout for plots otherwise use existing one ask If TRUE then prompt user before displaying each page of plots Default is dev interactive in R and interactive in S PLUS Graphical parameters Note The graphical implementation of Geweke s diagnostic was suggested by Steve Brooks See Also geweke diag heidel diag 19 heidel diag Heidelberger and Welch s convergence diagnostic Description heidel diag is a run length control diagnostic based on a criterion of relative accuracy for the estimate of the mean The default setting corresponds to a relative accuracy of two significant digits heidel diag also implements a convergence diagnostic and removes up to half the chain in order to ensure that the means are estimated from a chain that has converged Usage heidel diag x eps 0 1 pvalue 0 05 Arguments x An mcmc object eps Target value for ratio of halfwidth to sample
8. mean pvalue significance level to use Details The convergence test uses the Cramer von Mises statistic to test the null hypothesis that the sampled values come from a stationary distribution The test is successively applied firstly to the whole chain then after discarding the first 10 20 of the chain until either the null hypothesis is accepted or 50 of the chain has been discarded The latter outcome constitutes failure of the stationarity test and indicates that a longer MCMC run is needed If the stationarity test is passed the number of iterations to keep and the number to discard are reported The half width test calculates a 95 confidence interval for the mean using the portion of the chain which passed the stationarity test Half the width of this interval is compared with the estimate of the mean If the ratio between the half width and the mean is lower than eps the halfwidth test is passed Otherwise the length of the sample is deemed not long enough to estimate the mean with sufficient accuracy Theory The heidel diag diagnostic is based on the work of Heidelberger and Welch 1983 who com bined their earlier work on simulation run length control Heidelberger and Welch 1981 with the work of Schruben 1982 on detecting initial transients using Brownian bridge theory Note If the half width test fails then the run should be extended In order to avoid problems caused by sequential testing the test should
9. of the polynomial to fit to the periodogram max length The data x is aggregated if necessary by taking batch means so that the length of the series is less than max length If this is set to NULL no aggregation occurs Details The raw periodogram is calculated for the series x and a generalized linear model with family Gamma and log link is fitted to the periodogram The linear predictor is a polynomial in terms of the frequency The degree of the polynomial is determined by the parameter order Value A list with the following values spec The predicted value of the spectral density at frequency zero Theory Heidelberger and Welch 1991 observed that the usual non parametric estimator of the spectral den sity obtained by smoothing the periodogram is not appropriate for frequency zero They proposed an alternative parametric method which consisted of fitting a linear model to the log periodogram of the batched time series Some technical problems with model fitting in their original proposal can be overcome by using a generalized linear model Batching of the data originally proposed in order to save space has the side effect of flattening the spectral density and making a polynomial fit more reasonable Fitting a polynomial of degree zero is equivalent to using the batched means method Note The definition of the spectral density used here differs from that used by spec pgram We consider the frequency range to be betwee
10. plot of iterations vs sampled values for each variable in the chain with a separate plot per variable Usage traceplot x smooth FALSE col 1 6 type 1 xlab Iterations ylab Arguments x An mcmc or memc list object smooth draw smooth line through trace plot col graphical parameter see par type graphical parameter see plot xlab graphical parameter see plot ylab graphical parameter see plot further graphical parameters Note You can call this function directly but it is more usually called by the plot mcmc function See Also densplot plot mcmc trellisplots Trellis plots for mcmc objects Description These methods use the Trellis framework as implemented in the lattice package to produce space conserving diagnostic plots from mcmc and mcmc list objects The xyplot methods produce trace plots The densityplot methods and qqmath methods produce empirical density and prob ability plots The levelplot method depicts the correlation of the series The acfplot methods plot the auto correlation in the series Not yet available in S PLUS trellisplots Usage HH S3 method 39 for class mcemc densityplot x data HH S3 method outer aspect xy default scales list relation free start 1 thin 1 main attr x title xlab plot points rug subset for class mcmc list densityplot x data S3 method levelplot x S3 met
11. which to calculate the autocorrelation relative a logical flag TRUE if lags are relative to the thinning interval of the chain or FALSE if they are absolute difference in iteration numbers Value A vector or array containing the autocorrelations Author s Martyn Plummer See Also acf autocorr plot autocorr diag Autocorrelation function for Markov chains Description autocorr diag calculates the autocorrelation function for the Markov chain memc obj at the lags given by lags The lag values are taken to be relative to the thinning interval if relative TRUE Unlike autocorr if mcmc obj has many parmeters it only computes the autocorrelations with itself and not the cross correlations In cases where autocorr would return a matrix this function returns the diagonal of the matrix Hence it is more useful for chains with many parameters but may not be as helpful at spotting parameters If memc obj is of class mcmc list then the returned vector is the average autocorrelation across all chains Usage autocorr diag mcmc obj Arguments mcmc obj an object of class memc or mcmc list optional arguments to be passed to autocorr Value A vector containing the autocorrelations autocorr plot 5 Author s Russell Almond See Also autocorr acf autocorr plot autocorr plot Plot autocorrelations for Markov Chains Description Plots the autocorrelation function for each variable in each chain in x
12. 11 Brooks SP and Gelman A 1998 General methods for monitoring convergence of iterative simu lations Journal of Computational and Graphical Statistics 7 434 455 See Also gelman plot gelman plot Gelman Rubin Brooks plot Description This plot shows the evolution of Gelman and Rubin s shrink factor as the number of iterations increases Usage gelman plot x bin width 10 max bins 50 confidence 0 95 transform FALSE autoburnin TRUE auto layout TRUE ask col lty xlab ylab type auto layout gelman plot Arguments x an memc object bin width Number of observations per segment excluding the first segment which always has at least 50 iterations max bins Maximum number of bins excluding the last one confidence Coverage probability of confidence interval transform Automatic variable transformation see gelman diag autoburnin Remove first half of sequence see gelman diag If TRUE then set up own layout for plots otherwise use existing one ask Prompt user before displaying each page of plots Default is dev interactive in R and interactive in S PLUS col graphical parameter see par lty graphical parameter see par xlab graphical parameter see par ylab graphical parameter see par type graphical parameter see par further graphical parameters Details The Markov chain is divided into bins according to the arguments bin width and max bins Then the Gelman Ru
13. GS program No arguments are required Instead the user is prompted for the required information Usage read coda interactive Value An object of class memc list containing a representation of the data in one or more BUGS output files Note This function is normally called by the codamenu function but can also be used on a stand alone basis Author s Nicky Best Martyn Plummer References Spiegelhalter DJ Thomas A Best NG and Gilks WR 1995 BUGS Bayesian inference Using Gibbs Sampling Version 0 50 MRC Biostatistics Unit Cambridge 32 read openbugs See Also mcmc memc list read coda codamenu read openbugs Read CODA output files produced by OpenBUGS Description read openbugs reads Markov Chain Monte Carlo output in the CODA format produced by Open BUGS This is a convenience wrapper around the function read coda which allows you to read all the data output by OpenBUGS by specifying only the file stem Usage read openbugs stem start end thin quiet FALSE Arguments stem Character string giving the stem for the output files OpenBUGS produces files with names lt stem gt CODAindex txt lt stem gt CODAchain1 txt lt stem gt CODAchain2 txt start First iteration of chain end Last iteration of chain thin Thinning interval for chain quiet Logical flag If true a progress summary will be printed Value An object of class mcmc list containing output from all chains Author s
14. Package coda October 16 2015 Version 0 18 1 Date 2015 10 16 Title Output Analysis and Diagnostics for MCMC Depends R gt 2 14 0 Imports lattice Description Provides functions for summarizing and plotting the output from Markov Chain Monte Carlo MCMC simulations as well as diagnostic tests of convergence to the equilibrium distribution of the Markov chain License GPL gt 2 NeedsCompilation no Author Martyn Plummer aut cre trl Nicky Best aut Kate Cowles aut Karen Vines aut Deepayan Sarkar aut Douglas Bates aut Russell Almond aut Arni Magnusson aut Maintainer Martyn Plummer lt plummerm iarc fr gt Repository CRAN Date Publication 2015 10 16 20 00 43 R topics documented AS IS MCG e oon Gem ek by ee Oe Gy PE ee oe PS eS EE Ge a aulOCOl 6 6 peo ee Se Rhee eRe eH E AG X v Eee ee eee AULOCOM IAS oes oe ee Se AR Re o ROR Oe RE Ae AR autoco plot 22 2930 3 Bie ek ee AE LOD See e BRE RES We BA Ea E eus batchSE uuo UR pe Se RURUR RA RUE LS ew ee ee Gee Ke OR fous DUESZALS 2 C r7 COdB OPUONS se A ee eA Re E Index R topics documented codamenu 34 e a eee oS OR AL Bie be Soe RAL EUR o om ce as 9 ocn rcc 9 CEFOSSCO E Look e ehe E E SR E e a Oen eA AS d or RR 10 ChOSSCOM PIO 2 3 eee ed be parue Scd exuere dS eus duh tds 10 cumuplot lt ss ko o o E Roh Rom 84 be SOEUR R e bade Shee eo eae 11 densplol s s ees x Ier ce SER BAe ee Pe ce Beas she
15. ables nchain x returns the number of parallel chains plot mcmc 27 Usage niter x nvar x nchain x Arguments x An mcmc or memc list object Value A numeric vector of length 1 See Also mcmc memc list plot mcmc Summary plots of mcmc objects Description plot mcmc summarizes an mcmc or mcmc list object with a trace of the sampled output and a density estimate for each variable in the chain Usage S3 method for class mcmc plot x trace TRUE density TRUE smooth FALSE bwf auto layout TRUE ask dev interactive Arguments x an object of class mcmc or memc list trace Plot trace of each variable density Plot density estimate of each variable smooth Draw a smooth line through trace plots bwf Bandwidth function for density plots auto layout Automatically generate output format ask Prompt user before each page of plots Further arguments Author s Martyn Plummer 28 raftery diag See Also densplot traceplot raftery diag Raftery and Lewis s diagnostic Description raftery diag is a run length control diagnostic based on a criterion of accuracy of estimation of the quantile q It is intended for use on a short pilot run of a Markov chain The number of iterations required to estimate the quantile g to within an accuracy of r with probability p is calculated Separate calculations are performed for each variable within each chain If the number of it
16. amp ACIER a 11 etfectiVeSIZe i e uc ee A a oe URP Se Oe 12 pelmanmdiag 2 3x a eine eee EOS Ur IRL BRE ee eee dos 13 pelmatiplot cx ur memos Ge ee OE RUP Se Ox E RUE Rc ees 15 peweke diag gos suos Go Sah ge eR RR BER goes ao ERU E EUR eR RUE RR Oe E 17 peweke plot i e eee SY UU Sv erem eS oe Rd es KS 18 heidel didg 22k bsc x Duc X Row x doxes A ere ce e d 19 HD mtesival osa rmi REUS oU Fe we URS Feb ER NL ee Bede de re 20 JANE aon Sih Ste dpa eue AQ e UR ee bh Ge is Se BeOS e Eo ened See 21 MCMC owoeceboe e Rer ES ee x AE Bed A ee HS qase dog dus 21 MIGMIC CONVErt 5 e e 2 soe OH LO ESA OR S GR Ew EGE Shae ee Re yo 9 22 Meme list os 00m RS r 23 Meme SUBSE tepa uxo SUR e ew ADR game TR UR URDU IE D eU UR CRURA URS o6 24 momcUpsrade s i dix dee scs ee ee a eb e eoque db eu Sored e S 25 MEP a Be PUR ROS AU Ree th eode o eo de A RC AL oleo ee a 25 t ultidnenu ue dm er Rude Se eee oU di E dep ie RR Tod Rue 26 ner m PN 26 Plot MEMO 2 24 hook See es Pa HEED mae RARE Eh hue Hae RE DES 27 raftexy dl g soseo be e eo GA A bw Awe Bos PA eee s 28 read and check elos sr ugue eee e x Re ete hk Ah ee 29 I DHT imc Se daa BH Ga a a a Oa ag he 30 read coda interactive ee 31 redd openbugs s cd oh eek on eU a Sa ee xo a e e ee 22 rejectionRat icis omo kee ARES s GR Re P m Ce ee dU P PER RSG feas 33 spectrum dau ogg cese de Bho eA s SE OES A Ba RE ERR 33 spectrum ars def uei e dog ame aee qr exse Goa ge MUR Musei 35 SUMMA MEME
17. bin shrink factor is repeatedly calculated The first shrink factor is calculated with observations 1 50 the second with observations 1 50 n where n is the bin width the third contains samples 1 50 2n and so on Theory A potential problem with gelman diag is that it may mis diagnose convergence if the shrink factor happens to be close to 1 by chance By calculating the shrink factor at several points in time gelman plot shows if the shrink factor has really converged or whether it is still fluctuating References Brooks S P and Gelman A 1998 General Methods for Monitoring Convergence of Iterative Simulations Journal of Computational and Graphical Statistics 7 434 455 See Also gelman diag geweke diag 17 geweke diag Geweke s convergence diagnostic Description Geweke 1992 proposed a convergence diagnostic for Markov chains based on a test for equality of the means of the first and last part of a Markov chain by default the first 10 and the last 50 If the samples are drawn from the stationary distribution of the chain the two means are equal and Geweke s statistic has an asymptotically standard normal distribution The test statistic is a standard Z score the difference between the two sample means divided by its estimated standard error The standard error is estimated from the spectral density at zero and so takes into account any autocorrelation The Z score is calculated under the assump
18. c list Author s Martyn Plummer 24 mcmc subset See Also mcmc Examples data line x1 lt line 11 Select first chain x2 line 1 drop FALSE Select first var from all chains varnames x2 varnames line 1 TRUE meme subset Extract or replace parts of MCMC objects Description These are methods for subsetting mcmc objects You can select iterations using the first dimension and variables using the second dimension Selecting iterations will return a vector or matrix not an mcmc object If you want to do row subsetting of an mcmc object and preserve its dimensions use the window function Subsetting applied to an mcmc list object will simultaneously affect all the parallel chains in the object Usage S3 method for class mcmc x i j drop missing i S3 method for class mcmc list x i j drop TRUE Arguments x An meme object i Row to extract j Column to extract drop if TRUE the redundant dimensions are dropped See Also window mcmc mcmcUpgrade 25 mcmcUpgrade Upgrade mcmc objects in obsolete format Description In previous releases of CODA an mcmc object could be a single or multiple chains A new class mcmc list has now been introduced to deal with multiple chains and mcmc objects can only have data from a single chain Objects stored in the old format are now obsolete and must be upgraded Usage mcmcUpgrade x Arguments x an obsolete memc object Autho
19. ced by OpenBUGS and JAGS By default all of the data in the file is read but the arguments start end and thin may be used to read a subset of the data If the arguments given to start end or thin are incompatible with the data they are ignored Usage read coda output file index file start end thin quiet FALSE read jags file jags out start end thin quiet FALSE Arguments output file The name of the file containing the monitored output index file The name of the file containing the index showing which rows of the output file correspond to which variables file For JAGS output the name of the output file The extension out may be omitted There must be a corresponding ind file with the same file stem start First iteration of chain end Last iteration of chain thin Thinning interval for chain quiet Logical flag If true a progress summary will be printed read coda interactive 31 Value An object of class mcmc containing a representation of the data in the file Author s Karen Vines Martyn Plummer References Spiegelhalter DJ Thomas A Best NG and Gilks WR 1995 BUGS Bayesian inference Using Gibbs Sampling Version 0 50 MRC Biostatistics Unit Cambridge See Also mcmc read coda interactive read openbugs read coda interactive Read CODA output files interactively Description read coda interactive reads Markov Chain Monte Carlo output in the format produced by the classic BU
20. ed then both estimates are unbiased Otherwise the first method will underestimate the variance since the individual chains have not had time to range all over the stationary distribution and the second method will overestimate the variance since the starting points were chosen to be overdispersed The convergence diagnostic is based on the assumption that the target distribution is normal A Bayesian credible interval can be constructed using a t distribution with mean jt Sample mean of all chains combined and variance gt m V 67 4 mn and degrees of freedom estimated by the method of moments d 2x V Var V gelman plot 15 Use of the t distribution accounts for the fact that the mean and variance of the posterior distribution are estimated The convergence diagnostic itself is Values substantially above 1 indicate lack of convergence If the chains have not converged Bayesian credible intervals based on the t distribution are too wide and have the potential to shrink by this factor if the MCMC run is continued Note The multivariate a version of Gelman and Rubin s diagnostic was proposed by Brooks and Gelman 1998 Unlike the univariate proportional scale reduction factor the multivariate version does not include an adjustment for the estimated number of degrees of freedom References Gelman A and Rubin DB 1992 Inference from iterative simulation using multiple sequences Statistical Science 7 457 5
21. erations in data is too small an error message is printed indicating the minimum length of pilot run The minimum length is the required sample size for a chain with no correlation between consecutive samples Positive autocorrelation will increase the required sample size above this minimum value An estimate I the dependence factor of the extent to which autocorrela tion inflates the required sample size is also provided Values of I larger than 5 indicate strong autocorrelation which may be due to a poor choice of starting value high posterior correlations or stickiness of the MCMC algorithm The number of burn in iterations to be discarded at the beginning of the chain is also calculated Usage raftery diag data q 0 025 r 0 005 s 0 95 converge eps 0 001 Arguments data an mcmc object q the quantile to be estimated r the desired margin of error of the estimate S the probability of obtaining an estimate in the interval q r q r converge eps Precision required for estimate of time to convergence Value A list with class raftery diag A print method is available for objects of this class the contents of the list are tspar The time series parameters of data params A vector containing the parameters r s and q Niters The number of iterations in data resmatrix A 3 d array containing the results M the length of burn in N the required sample size N min the minimum sample size based on zero autocorrela
22. from the range calculations other arguments passed to the lattice function Documentation of the corre sponding generics in the lattice package should be consulted for possible ar guments indices of the subset of the series to plot The default is constructed from the start and thin arguments 42 varnames Value An object of class trellis The relevant update method can be used to update components of the object and the print method usually called by default will plot it on an appropriate plotting device Author s Deepayan Sarkar lt Deepayan Sarkar R project org gt See Also Lattice for a brief introduction to lattice displays and links to further documentation Examples data line Not run xyplot line xyplot line 1 start 10 densityplot line start 10 qqmath line start 10 levelplot line 2 acfplot line outer TRUE End Not run varnames Named dimensions of MCMC objects Description varnames returns the variable names and chanames returns the chain names or NULL if these are not set If allow null FALSE then NULL values will be replaced with canonical names Usage varnames x allow null TRUE chanames x allow null TRUE varnames x value chanames x value Arguments x an mcmc or memc list object allow null Logical argument that determines whether the function may return NULL value A character vector or NULL window mcmc 43 Value A charac
23. hod outer FALSE groups outer aspect xy default scales list relation free start 1 thin 1 main attr x title xlab plot points rug subset for class mcmc data main attr x title start 1 thin 1 xlab ylab cuts 10 at col regions topo colors 100 subset for class mcmc qqmath x data HH S3 method outer aspect xy default scales list y list relation free prepanel prepanel qqmathline start 1 thin 1 main attr x title ylab subset for class mcmc list qqmath x data outer FALSE groups outer aspect xy default scales list y list relation free prepanel prepanel qqmathline start 1 thin 1 main attr x title 40 ylab wee subset HH S3 method for class mcmc xyplot x data outer layout c 1 nvar x default scales list y list relation free type l start 1 thin 1 xlab ylab main subset Iteration number nn attr x title S3 method for class mcmc list xyplot x data outer FALSE groups outer default scales list y list relation free aspect xy layout c 1 nvar x type l start 1 thin 1 xlab Iteration number ylab main attr x title subset acfplot x data ylab xlab main subset La S3
24. hod for class mcmc list as array x drop memce list 23 Arguments x An meme or memc list object iters logical flag add column for iteration number chains logical flag add column for chain number if mcmc list drop logical flag if TRUE the result is coerced to the lowest possible dimension optional arguments to the various methods See Also as matrix as array as mcmc mcmc list Replicated Markov Chain Monte Carlo Objects Description The function mcmc list is used to represent parallel runs of the same chain with different starting values and random seeds The list must be balanced each chain in the list must have the same iterations and the same variables Diagnostic functions which act on mcmc objects may also be applied to mcmc list objects In general the chains will be combined if this makes sense otherwise the diagnostic function will be applied separately to each chain in the list Since all the chains in the list have the same iterations a single time dimension can be ascribed to the list Hence there are time series methods time window start end frequency and thin for memc list objects Anmemc list can be indexed as if it were a single memc object using the operator see examples below The operator selects a single memc object from the list Usage mcmc list as mcmc list x is mcmc list x Arguments a list of mcmc objects x an object that may be coerced to mcm
25. method for class mcmc acfplot x data outer prepanel panel type h aspect xy start 1 thin 1 lag max NULL Autocorrelation Lag i attr x title S3 method for class mcmc list acfplot x data outer FALSE groups prepanel panel type if groups b else h aspect xy start 1 thin 1 lag max NULL ylab Autocorrelation xlab Lag main attr x title louter trellisplots trellisplots 41 subset Arguments x data outer groups aspect default scales type thin start plot points layout xlab ylab main cuts at col regions lag max prepanel panel subset an mcmc or memc list object ignored present for consistency with generic for the mcmc list methods a logical flag to control whether multiple runs of a series are displayed in the same panel they are if FALSE not if TRUE If specified in the mcmc methods this argument is ignored with a warning for the mcmc list methods a logical flag to control whether the underlying lattice call will be supplied a groups arguments indicating which run a data point originated from The panel function is responsible for handling such an argument and will usually differentiate runs within a panel by using different graphical parameters When outer FALSE the default of groups is TRUE if the corresponding default panel function is able to make use of such i
26. n 0 and 0 5 not between O and frequency x 2 The model fitting may fail on chains with very high autocorrelation References Heidelberger P and Welch P D A spectral method for confidence interval generation and run length control in simulations Communications of the ACM Vol 24 pp233 245 1981 See Also spectrum spectrum0 ar glm spectrum0 ar 35 spectrum ar Estimate spectral density at zero Description The spectral density at frequency zero is estimated by fitting an autoregressive model spectrum x length x estimates the variance of mean x Usage spectrum0 ar x Arguments x A time series Details The ar function to fit an autoregressive model to the time series x For multivariate time series separate models are fitted for each column The value of the spectral density at zero is then given by a well known formula Value A list with the following values spec The predicted value of the spectral density at frequency zero order The order of the fitted model Note The definition of the spectral density used here differs from that used by spec pgram We consider the frequency range to be between 0 and 0 5 not between O and frequency x 2 See Also spectrum spectrum0 glm 36 thin summary mcmc Summary statistics for Markov Chain Monte Carlo chains Description summary mcmc produces two sets of summary statistics for each variable Mean standard deviation nai
27. nformation When outer FALSE groups TRUE will be ignored with a warning controls the physical aspect ratio of the panel See xyplot for details The default for these methods is chosen carefully check what the default plot looks like before changing this parameter this parameter provides a reasonable default value of the scales parameter for the method It is unlikely that a user will wish to change this parameter Pass a value for scales see xyplot instead which will override values specified here a character vector that determines if lines points etc are drawn on the panel The default values for the methods are carefully chosen See panel xyplot for possible values an optional thinning interval that is applied before the plot is drawn an optional value for the starting point within the series Values before the start ing point are considered part of the burn in of the series and dropped character argument giving the style in which points are added to the plot See panel densityplot for details a method specific default for the layout argument to the lattice functions Used to provide default axis annotations and plot labels defines number and location of values where colors change color palette used maximum lag for which autocorrelation is computed By default the value cho sen by acf is used suitable prepanel and panel functions for acfplot The prepanel function omits the lag 0 auto correlation which is always 1
28. not be repeated too frequently Heidelberger and Welch 1981 suggest increasing the run length by a factor I gt 1 5 each time so that estimate has the same reasonably large proportion of new data 20 HPDinterval References Heidelberger P and Welch PD A spectral method for confidence interval generation and run length control in simulations Comm ACM 24 233 245 1981 Heidelberger P and Welch PD Simulation run length control in the presence of an initial transient Opns Res 31 1109 44 1983 Schruben LW Detecting initialization bias in simulation experiments Opns Res 30 569 590 1982 HPDinterval Highest Posterior Density intervals Description Create Highest Posterior Density HPD intervals for the parameters in an MCMC sample Usage HPDinterval obj prob 95 S3 method for class mcmc HPDinterval obj prob 95 S3 method for class mcmc list HPDinterval obj prob 0 95 Arguments obj The object containing the MCMC sample usually of class mcmc or mcmc list prob A numeric scalar in the interval 0 1 giving the target probability content of the intervals The nominal probability content of the intervals is the multiple of 1 nrow obj nearest to prob Optional additional arguments for methods None are used at present Details For each parameter the interval is constructed from the empirical cdf of the sample as the shortest interval for which the difference in
29. nu interface The coda options function behaves just like the options function in the base library with the additional feature that coda options default TRUE will reset all options to the default values Options can be pretty printed using the display coda options function which groups the op tions into sections Available options are bandwidth Bandwidth function used when smoothing samples to produce density estimates De faults to Silverman s Rule of thumb combine corr Logical option that determines whether to combine multiple chains when calculating cross correlations combine plots Logical option that determines whether to combine multiple chains when plotting combine plots Logical option that determines whether to combine multiple chains when calculat ing summary statistics data saved For internal use only coda options densplot Logical option that determines whether to plot a density plot when plot methods are called for mcmc objects digits Number of significant digits to use when printing fracl For Geweke diagnostic fraction to use from start of chain Defaults to 0 1 frac2 For Geweke diagnostic fraction to use from end of chain Default to 0 5 gr bin For Geweke Brooks plot number of iterations to use per bin gr max For Geweke Brooks plot maximum number of bins to use This option overrides gr bin halfwidth For Heidelberger and Welch diagnostic the target value for the ratio of half width
30. ov Chain Monte Carlo in Practice Chapman and Hall 45 58 See Also spectrum0 ar ef fectiveSize summary mcmc bugs2jags Convert WinBUGS data file to JAGS data file Description bugs2jags converts a WinBUGS data in the format called S Plus i e the format created by the dput function and writes it in dump format used by JAGS NB WinBUGS stores its arrays in row order This is different from R and JAGS which both store ar rays in column order This difference is taken into account by bugs2jags which will automatically reorder the data in arrays without changing the dimension Not yet available in S PLUS Usage bugs2jags infile outfile coda options 7 Arguments infile name of the input file outfile name of the output file Note If the input file is saved from WinBUGS it must be saved in plain text format The default format for files saved from WinBUGS is a binary compound document format with extension odc that cannot be read by bugs2jags Author s Martyn Plummer References Spiegelhalter DJ Thomas A Best NG and Lunn D 2003 WinBUGS version 1 4 user manual MRC Biostatistics Unit Cambridge UK See Also dput dump coda options Options settings for the codamenu driver Description coda options is a utility function that queries and sets options for the codamenu function These settings affect the behaviour of the functions in the coda library only when they are called via the codame
31. r s Martyn Plummer See Also mcmc mcpar Mcpar attribute of MCMC objects Description The mcpar attribute of an MCMC object gives the start iteration the end iteration and the thinning interval of the chain It resembles the tsp attribute of time series ts objects Usage mcpar x Arguments x An mcmcm or memc list object See Also ts mcmc memc list 26 nchain multi menu Choose multiple options from a menu Description multi menu presents the user with a menu of choices labelled from 1 to the number of choices The user may choose one or more options by entering a comma separated list A range of values may n n also be specified using the operator Mixed expressions such as 1 3 5 6 are permitted If allow zero is set to TRUE one can select 0 to exit without choosing an item Usage multi menu choices title header allow zero TRUE Arguments choices Character vector of labels for choices title Title printed before menu header Character vector of length 2 giving column titles allow zero Permit 0 as an acceptable response Value Numeric vector giving the numbers of the options selected or O if no selection is made Author s Martyn Plummer See Also menu nchain Dimensions of MCMC objects Description These functions give the dimensions of an MCMC object niter x returns the number of iterations nvar x returns the number of vari
32. scorr 10 Topic ts as ts mcmc 3 autocorr 3 autocorr diag 4 batchSE 5 effectiveSize 12 mcmc 21 mcmc list 23 mcmc subset 24 mcmcUpgrade 25 mcpar 25 nchain 26 rejectionRate 33 spectrumo 33 spectrum ar 35 thin 36 time mcmc 37 window mcmc 43 Topic univar HPDinterval 20 summary mcmc 36 Topic utilities as ts mcmc 3 coda options 7 codamenu 9 multi menu 26 read and check 29 Coda Options coda options 7 L 24 mcmc memc subset 24 acf 4 5 41 acfplot trellisplots 38 as array 23 as array mcmc list mcmc convert 22 as matrix 23 as matrix mcmc mcmc convert 22 as mcmc 23 as mcmc mcmc 21 as mcmc list mcmc list 23 as mcmc mcmc list mcmc convert 22 as ts 3 as ts mcmc 3 autocorr 3 5 10 autocorr diag 4 autocorr plot 4 5 5 INDEX batchSE 5 bugs2jags 6 chanames varnames 42 chanames lt varnames 42 coda options 7 codamenu 9 32 Cramer 9 crosscorr 10 71 crosscorr plot 0 10 cumuplot 11 density 12 densityplot mcmc trellisplots 38 densplot 11 26 38 display coda options coda options 7 dput 7 dump 7 effectiveSize 6 12 end mcmc time mcmc 37 frequency 37 frequency mcmc time mcmc 37 gelman diag 13 16 gelman plot 15 15 geweke diag 17 18 geweke plot 17 18 glm 34 35 heidel diag 19 HPDinterval 20 image 71 is mcmc mcmc 21 is mcmc list mcmc list 23 Lattice 42 levelplot mcmc
33. ter vector or NULL See Also mcmc memc list window mcmc Time windows for mcmc objects Description window mcmc is a method for mcmc objects which is normally called by the generic function window In addition to the generic parameters start and end the additional parameter thin may be used to thin out the Markov chain Setting thin k selects every kth iteration starting with the first Note that the value of thin is absolute not relative The value supplied given to the parameter thin must be a multiple of thin x Values of start end and thin which are inconsistent with x are ignored but a warning message is issued Usage S3 method for class mcmc window x start end thin Arguments x an mcmc object start the first iteration of interest end the last iteration of interest thin the required interval between successive samples futher arguments for future methods See Also window thin Index Topic array crosscorr 10 mcemc convert 22 Topic datasets line 21 Topic distribution Cramer 9 Topic file bugs2jags 6 read coda 30 read coda interactive 31 read openbugs 32 Topic hplot autocorr plot 5 crosscorr plot 10 cumuplot 11 densplot 11 gelman plot 15 geweke plot 18 plot memc 27 traceplot 38 trellisplots 38 Topic htest gelman diag 13 geweke diag 17 heidel diag 19 HPDinterval 20 raftery diag 28 Topic manip varnames 42 Topic multivariate cros
34. the ecdf values of the endpoints is the nominal probability Assuming that the distribution is not severely multimodal this is the HPD interval Value For an mcmc object a matrix with columns lower and upper and rows corresponding to the parameters The attribute Probability is the nominal probability content of the intervals A list of such matrices is returned for an mcmc list object Author s Douglas Bates line 21 Examples data line HPDinterval line line Simple linear regression example Description Sample MCMC output from a simple linear regression model given in the BUGS manual Usage data line Format An mcmc object Source Spiegelhalter D J Thomas A Best N G and Gilks W R 1995 BUGS Bayesian inference using Gibbs Sampling Version 0 5 MRC Biostatistics Unit Cambridge mcmc Markov Chain Monte Carlo Objects Description The function meme is used to create a Markov Chain Monte Carlo object The data are taken to be a vector or a matrix with one column per variable An mcmc object may be summarized by the summary function and visualized with the plot func tion MCNC objects resemble time series ts objects and have methods for the generic functions time start end frequency and window Usage mcmc data NA start 1 end numeric 0 thin 1 as mcmc x is mcmc x 22 Arguments data start end thin X Note mcmc convert
35. tion and I M N Nmin the dependence factor read and check 29 Theory The estimated sample size for variable U is based on the process Z d U lt u where d is the indicator function and u is the qth quantile of U The process Z is derived from the Markov chain data by marginalization and truncation but is not itself a Markov chain However Z may behave as a Markov chain if it is sufficiently thinned out raftery diag calculates the smallest value of thinning interval k which makes the thinned chain Z behave as a Markov chain The required sample size is calculated from this thinned sequence Since some data is thrown away the sample size estimates are conservative The criterion for the number of burn in iterations m to be discarded is that the conditional distri bution of ZE given Zo should be within converge eps of the equilibrium distribution of the chain ZE Note raftery diag is based on the FORTRAN program gibbsit written by Steven Lewis and available from the Statlib archive References Raftery A E and Lewis S M 1992 One long run with diagnostics Implementation strategies for Markov chain Monte Carlo Statistical Science 7 493 497 Raftery A E and Lewis S M 1995 The number of iterations convergence diagnostics and generic Metropolis algorithms n Practical Markov Chain Monte Carlo W R Gilks D J Spiegel halter and S Richardson eds London U K Chapman and Hall
36. tion that the two parts of the chain are asymptotically independent which requires that the sum of frac1 and frac2 be strictly less than 1 Usage geweke diag x fracl 0 1 frac2 0 5 Arguments x an mcmc object fracl fraction to use from beginning of chain frac2 fraction to use from end of chain Value Z scores for a test of equality of means between the first and last parts of the chain A separate statistic is calculated for each variable in each chain References Geweke J Evaluating the accuracy of sampling based approaches to calculating posterior mo ments In Bayesian Statistics 4 ed JM Bernado JO Berger AP Dawid and AFM Smith Clarendon Press Oxford UK See Also geweke plot 18 geweke plot geweke plot Geweke Brooks plot Description If geweke diag indicates that the first and last part of a sample from a Markov chain are not drawn from the same distribution it may be useful to discard the first few iterations to see if the rest of the chain has converged This plot shows what happens to Geweke s Z score when successively larger numbers of iterations are discarded from the beginning of the chain To preserve the asymptotic conditions required for Geweke s diagnostic the plot never discards more than half the chain The first half of the Markov chain is divided into nbins 1 segments then Geweke s Z score is repeatedly calculated The first Z score is calculated with all iterations in the chain
37. to sample mean lowess Logical option that controls whether to plot a smooth line through a trace plot when plotting MCMC output q For Raftery and Lewis diagnostic the target quantile to be estimated r For Raftery and Lewis diagnostic the required precision s For Raftery and Lewis diagnostic the probability of obtaining an estimate in the interval q r q r quantiles Vector of quantiles to print when calculating summary statistics for MCMC output trace Logical option that determines whether to plot a trace of the sampled output when plotting MCMC output user layout Logical option that determines whether current value of par mfrow should be used for plots TRUE or whether the optimal layout should be calculated FALSE Usage coda options display coda options stats FALSE plots FALSE diags FALSE Coda Options Coda Options Default Arguments stats logical flag show summary statistic options plots logical flag show plotting options diags logical flag show plotting options list of options See Also options codamenu 9 codamenu Main menu driver for the coda package Description codamenu presents a simple menu based interface to the functions in the coda package It is de signed for users who know nothing about the R S language Usage codamenu Author s Kate Cowles Nicky Best Karen Vines Martyn Plummer Cramer The Cramer von Mises Distribution Description Distrib
38. trellisplots 38 line 21 meme 21 24 25 27 31 32 36 43 mcmc convert 22 mcmc list 22 23 25 27 32 36 43 mcmc subset 24 mcmcUpgrade 22 25 mcpar 25 menu 26 multi menu 26 45 nchain 26 niter nchain 26 nvar nchain 26 options 8 panel densityplot 47 panel xyplot 47 pcramer Cramer 9 plot memc 12 22 27 38 plot mcmc list mcmc list 23 print 42 print mcmc memc 21 qqmath mcmc trellisplots 38 raftery diag 28 read and check 29 read coda 30 32 read coda interactive 3 31 read jags read coda 30 read openbugs 31 32 rejectionRate 33 spectrum 34 35 spectrum 33 35 spectrum0 ar 6 13 34 35 start 37 start mcmc time mcmc 37 summary mcmc 6 22 36 thin 22 36 37 43 thin mcmc time mcmc 37 time 37 time mcmc 37 topo colors 71 traceplot 28 38 trellisplots 38 ts 25 update 42 varnames 42 varnames lt varnames 42 window 43 window mcmc 22 24 43 xyplot 47 xyplot mcmc trellisplots 38
39. ts x an mcmc or memc list object col color palette to use graphical parameters cumuplot 11 See Also crosscorr image topo colors cumuplot Cumulative quantile plot Description Plots the evolution of the sample quantiles as a function of the number of iterations Usage cumuplot x probs c 0 025 0 5 0 975 ylab lty c 2 1 lwd c 1 2 type 1 ask auto layout TRUE col 1 Arguments x an mcmc object probs vector of desired quantiles ylab lty lwd type col graphical parameters auto layout If TRUE then set up own layout for plots otherwise use existing one ask If TRUE then prompt user before displaying each page of plots Default is dev interactive in R and interactive in S PLUS further graphical parameters Author s Arni Magnusson densplot Probability density function estimate from MCMC output Description Displays a plot of the density estimate for each variable in x calculated by the density function Usage densplot x show obs TRUE bwf ylim xlab ylab nn type 1 main 12 effectiveSize Arguments x An mcmc or memc list object show obs Show observations along the x axis bwf Function for calculating the bandwidth If omitted the bandwidth is calculate by 1 06 times the minimum of the standard deviation and the interquartile range divided by 1 34 times the sample size to the negative one fifth power ylim Limits on y axis See plot
40. ution function of the Cramer von Mises distribution Usage pcramer q eps Arguments q vector of quantiles eps accuracy required Value pcramer gives the distribution function References Anderson TW and Darling DA Asymptotic theory of certain goodness of fit criteria based on stochastic processes Ann Math Statist 23 192 212 1952 Csorgo S and Faraway JJ The exact and asymptotic distributions of the Cramer von Mises statistic J Roy Stat Soc B 58 221 234 1996 10 crosscorr plot crosscorr Cross correlations for MCMC output Description crosscorr calculates cross correlations between variables in Markov Chain Monte Carlo output If x is an mcmc list then all chains in x are combined before calculating the correlation Usage crosscorr x Arguments x an memc or memc list object Value A matrix or 3 d array containing the correlations See Also crosscorr plot autocorr crosscorr plot Plot image of correlation matrix Description crosscorr plot provides an image of the correlation matrix for x If x is an mcmc list object then all chains are combined The range 1 1 is divided into a number of equal length categories given by the length of col and assigned the corresponding color By default topographic colours are used as this makes it easier to distinguish positive and negative correlations Usage crosscorr plot x col topo colors 10 Argumen
41. variate a logical flag indicating whether the multivariate potential scale reduction factor should be calculated for multivariate chains Value An object of class gelman diag This is a list with the following elements psrf A list containing the point estimates of the potential scale reduction factor la belled Point est and their upper confidence limits labelled Upper C I mpsrf The point estimate of the multivariate potential scale reduction factor This is NULL if there is only one variable in x The gelman diag class has its own print method Theory Gelman and Rubin 1992 propose a general approach to monitoring convergence of MCMC out put in which m gt 1 parallel chains are run with starting values that are overdispersed relative to the posterior distribution Convergence is diagnosed when the chains have forgotten their initial values and the output from all chains is indistinguishable The gelman diag diagnostic is applied to a single variable from the chain It is based a comparison of within chain and between chain variances and is similar to a classical analysis of variance There are two ways to estimate the variance of the stationary distribution the mean of the empirical variance within each chain W and the empirical variance from all chains combined which can be expressed as 2 n n n n where n is the number of iterations and B n is the empirical between chain variance If the chains have converg
42. ve standard error of the mean ignoring autocorrelation of the chain and time series standard error based on an estimate of the spectral density at O Quantiles of the sample distribution using the quantiles argument Usage S3 method for class mcmc summary object quantiles c 0 025 0 25 0 5 0 75 0 975 Arguments object an object of class memc or mcmc list quantiles a vector of quantiles to evaluate for each variable a list of further arguments Author s Martyn Plummer See Also mcmc memc list thin Thinning interval Description thin returns the interval between successive values of a time series thin x is equivalent to 1 frequency x This is a generic function Methods have been implemented for mcmc objects Usage thin x time mcmc Arguments x a regular time series a list of arguments Author s Martyn Plummer See Also time 37 time mcmc Time attributes for mcmc objects Description These are methods for mcmc objects for the generic time series functions Usage HH S3 method for class mcmc time x S3 method for class mcmc start x S3 method for class mcmc end x S3 method for class mcmc thin x Arguments x an mcmc or memc list object extra arguments for future methods See Also time start frequency thin 38 trellisplots traceplot Trace plot of MCMC output Description Displays a
43. window xlab X axis label By default this will show the sample size and the bandwidth used for smoothing See plot ylab Y axis label By default this is blank See plot type Plot type See plot main An overall title for the plot See title Further graphical parameters Note You can call this function directly but it is more usually called by the plot mcmc function If a variable is bounded below at 0 or bounded in the interval 0 1 then the data are reflected at the boundary before being passed to the density function This allows correct estimation of a non zero density at the boundary See Also density plot mcmc effectiveSize Effective sample size for estimating the mean Description Sample size adjusted for autocorrelation Usage effectiveSize x Arguments x An mcmc or memc list object gelman diag 13 Details For a time series x of length N the standard error of the mean is the square root of var x n where n is the effective sample size n N only when there is no autocorrelation Estimation of the effective sample size requires estimating the spectral density at frequency zero This is done by the function spectrum0 ar For a mcmc list object the effective sizes are summed across chains To get the size for each chain individually use lapply x effectiveSize Value A vector giving the effective sample size for each column of x See Also spectrum0 ar gelman diag Gelman and Rubin s convergence diagnostic
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