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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PRIOR/HYPERPRIOR Statement
PRIOR parameter-list ~distribution ;
HYPERPRIOR parameter-list ~distribution ;
HYPER parameter-list ~distribution ;
The PRIOR statement specifies the prior distribution of the model parameters. You must specify a single parameter or a list of parameters, a tilde ~, and then a distribution with its parameters.
You can specify multiple PRIOR statements to define models with multiple prior components. Your model can have as many hierarchical levels as you want. But in many cases, such as random-effects models, it is better to use the RANDOM statements to build up the model hierarchy. The log of the prior is the sum of the log prior values from each of the PRIOR statements. Similar to the MODEL statement, you can use the PRIOR statement to specify marginal or conditional prior distributions. See the section MODEL Statement for the names of the standard distributions and the section Standard Distributions for density specification.
The PRIOR statements are processed twice at every Markov chain simulation—that is, twice per pass through the data set. The statements are called at the first and the last observation of the data set, just as the BEGINNODATA and ENDNODATA statements are processed. If you run a Monte Carlo simulation that is data-independent, you can specify the NOLOGDIST option in the PROC MCMC statement to omit the calculation of the prior distribution. Omitting this calculation enables PROC MCMC to run faster.
The HYPERPRIOR statement is treated internally the same as the PRIOR statement. It provides a notational convenience in case you want to fit a multilevel hierarchical model. It specifies the hyperprior distribution of the prior distribution parameters. The log of the hyperprior is the sum of the log hyperprior values from each of the HYPERPRIOR statements.
Parameters in the PRIOR statements can appear as hyperparameters in the RANDOM statement. The reverse is not allowed: random-effects parameters cannot be hyperparameters in a PRIOR statement.
You can have a program that contains a RANDOM statement but no PRIOR statements. (In SAS 9.3 and earlier, each program had to contain a PRIOR statement.) A program that contains a RANDOM statement but no PRIOR statements could be a random-effects model with no fixed-effects parameters or hyperparameters to the random effects. A MODEL statement is still required in every program.