The MCMC Procedure
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Overview
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Getting Started
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Syntax
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DetailsHow PROC MCMC WorksBlocking of ParametersSampling MethodsTuning the Proposal DistributionDirect SamplingConjugate SamplingInitial Values of the Markov ChainsAssignments of ParametersStandard DistributionsUsage of Multivariate DistributionsSpecifying a New DistributionUsing Density Functions in the Programming StatementsTruncation and CensoringSome Useful SAS FunctionsMatrix Functions in PROC MCMCCreate Design MatrixModeling Joint LikelihoodRegenerating Diagnostics PlotsCaterpillar PlotAutocall Macros for PostprocessingGamma and Inverse-Gamma DistributionsPosterior Predictive DistributionHandling of Missing DataFunctions of Random-Effects ParametersFloating Point Errors and OverflowsHandling Error MessagesComputational ResourcesDisplayed OutputODS Table NamesODS Graphics
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ExamplesSimulating Samples From a Known DensityBox-Cox TransformationLogistic Regression Model with a Diffuse PriorLogistic Regression Model with Jeffreys’ PriorPoisson RegressionNonlinear Poisson Regression ModelsLogistic Regression Random-Effects ModelNonlinear Poisson Regression Multilevel Random-Effects ModelMultivariate Normal Random-Effects ModelMissing at Random AnalysisNonignorably Missing Data (MNAR) AnalysisChange Point ModelsExponential and Weibull Survival AnalysisTime Independent Cox ModelTime Dependent Cox ModelPiecewise Exponential Frailty ModelNormal Regression with Interval CensoringConstrained AnalysisImplement a New Sampling AlgorithmUsing a Transformation to Improve MixingGelman-Rubin Diagnostics
- References
PROC MCMC assigns a name to each table it creates. You can use these names to refer to the table when you use the Output Delivery System (ODS) to select tables and create output data sets. These names are listed in Table 61.48. For more information about ODS, see Chapter 21: Statistical Graphics Using ODS.
Table 61.48: ODS Tables Produced in PROC MCMC
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ODS Table Name |
Description |
Statement or Option |
|---|---|---|
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Autocorrelation statistics for each parameter |
DIAGNOSTICS=AUTOCORR |
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History of burn-in phase sampling |
MCHISTORY=BRIEF | DETAILED |
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Optimization convergence status |
PROPCOV= |
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Correlation matrix of the posterior samples |
STATS=CORR |
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Covariance matrix of the posterior samples |
STATS=COV |
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Deviance information criterion |
DIC |
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Effective sample size for each parameter |
Default |
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Monte Carlo standard error for each parameter |
DIAGNOSTICS=MCSE |
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Geweke diagnostics for each parameter |
DIAGNOSTICS=GEWEKE |
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Heidelberger-Welch diagnostics for each parameter |
DIAGNOSTICS=HEIDEL |
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Optimization input table |
PROPCOV= |
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Optimization iteration history |
PROPCOV= |
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Optimization results table |
PROPCOV= |
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Response variable, number of missing observations, missing observation indices, and sampling algorithm |
Default with sampling of missing values |
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Number of observations |
Default |
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Parameter values after either optimization |
PROPCOV= |
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Covariance used in proposal distribution after optimization |
PROPCOV= |
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Summary of the PARMS, BLOCKING, PRIOR, sampling method, and initial value specification |
Default |
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Parameter values after the tuning phase |
INIT=PINIT |
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Posterior samples for each parameter |
(For ODS output data set only) |
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Equal-tail and HPD intervals for each parameter |
STATISTICS=INTERVAL |
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Basic posterior statistics for each parameter, including sample size, mean, standard deviation, and HPD intervals |
Default |
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Basic posterior statistics for each parameter, including sample size, mean, standard deviation, and percentiles |
STATISTICS=SUMMARY |
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Equal-tail and HPD intervals for each prediction |
Default with any PREDDIST statement |
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Basic posterior statistics for each prediction |
Default with any PREDDIST statement |
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Optimization table |
PROPCOV= |
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Random effect, subject values, number of observations in each unique subject value, and corresponding observation indices |
REOBSINFO |
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Random effect, sampling method, subject variable, number of subjects, unique values of the subject variable, and prior distribution of the random effect |
Default with any RANDOM statement |
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Raftery-Lewis diagnostics for each parameter |
DIAGNOSTICS=RAFTERY |
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History of main phase sampling |
MCHISTORY=BRIEF | DETAILED |
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Proposal covariance matrix (for continuous parameters) after the tuning phase |
INIT=PINIT |
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Proposal probability vector (for discrete parameters) after the tuning phase |
INIT=PINIT and DISCRETE=GEO |
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History of proposal distribution tuning |
MCHISTORY=BRIEF | DETAILED |