The MCMC Procedure
-
Overview
-
Getting Started
-
Syntax
-
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
-
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
The word “direct” is reserved for sampling that is done directly from the prior distribution of a model or a random-effects parameter or from the sampling distribution of a missing data variable. If the parameter is updated via sampling from its full conditional posterior distribution, the sampling method is referred to as conjugate sampling. (See the section Conjugate Sampling.)
Whenever a parameter does not appear in the hierarchy of another parameter in the model, PROC MCMC samples directly from its distribution. For a model parameter or a random-effects parameter, this distribution is its prior distribution. For a missing data variable, this distribution is the sampling distribution of the response variable. Therefore, direct sampling takes place most frequently in data-independent Monte Carlo simulations or the sampling of missing response variables.