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
In general, you cannot alter the values of any model parameters in PROC MCMC. For example, the following assignment statement produces an error:
parms alpha; alpha = 27;
This restriction prevents incorrect calculation of the posterior density—assignments of parameters in the program would override the parameter values generated by PROC MCMC and lead to an incorrect value of the density function.
However, you can modify parameter values and assign initial values to parameters within the block defined by the BEGINCNST and ENDCNST statements. The following syntax is allowed:
parms alpha; begincnst; alpha = 27; endcnst;
The initial value of alpha is 27. Assignments within the BEGINCNST/ENDCNST block override initial values specified in the PARMS statement. For example, with the following statements, the Markov chain starts at alpha 
, not 23.
parms alpha 23; begincnst; alpha = 27; endcnst;
This feature enables you to systematically assign initial values. Suppose that z is an array parameter of the same length as the number of observations in the input data set. You want to start the Markov
chain with each 
having a different value depending on the data set variable y. The following statements set 
for the first half of the observations and 
for the rest:
/* a rather artificial input data set. */
data inputdata;
do ind = 1 to 10;
y = rand('normal');
output;
end;
run;
proc mcmc data=inputdata;
array z[10];
begincnst;
if ind <= 5 then z[ind] = abs(y);
else z[ind] = 2.3;
endcnst;
parms z:;
prior z: ~ normal(0, sd=1);
model general(0);
run;
Elements of z are modified as PROC MCMC executes the programming statements between the BEGINCNST and ENDCNST statements. This feature could be useful when you use the GENERAL function and you find that the PARMS statements are too cumbersome for assigning starting values.