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
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The following statements are available in the MCMC procedure. Items within < > are optional.
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PROC MCMC <options>;
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ARRAY arrayname [ dimensions ] <$> <variables-and-constants>;
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BY variables;
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MODEL variable ~distribution <options>;
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PARMS parameter <=> number </ options>;
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PREDDIST <'label'> OUTPRED=SAS-data-set <options>;
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PRIOR/HYPERPRIOR parameter ~distribution;
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RANDOM random-effects-specification </ options>;
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UDS subroutine-name (subroutine-argument-list);
The PARMS statements declare parameters in the model and assign optional starting values for the Markov chain. The PRIOR/HYPERPRIOR statements specify the prior distributions of the parameters. The MODEL statements specify the log-likelihood functions for the response variables. These statements form the basis of most Bayesian models.
In addition, you can use the ARRAY statement to define constant or parameter arrays, the BEGINCNST/ENDCNST and BEGINNODATA/ENDNODATA statements to omit unnecessary evaluation and reduce simulation time, the PREDDIST statement to generate samples from the posterior predictive distribution, the program statements to specify more complicated models that you want to fit, the RANDOM statement to specify random effects and their prior distributions, and the UDS statement to define your own Gibbs samplers to sample parameters in the model.
The following sections provide a description of each of these statements.