The MCMC Procedure
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Overview
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Getting Started
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Syntax
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Details
How PROC MCMC Works Blocking of Parameters Sampling Methods Tuning the Proposal Distribution Conjugate Sampling Initial Values of the Markov Chains Assignments of Parameters Standard Distributions Usage of Multivariate Distributions Specifying a New Distribution Using Density Functions in the Programming Statements Truncation and Censoring Some Useful SAS Functions Matrix Functions in PROC MCMC Create Design Matrix Modeling Joint Likelihood Regenerating Diagnostics Plots Caterpillar Plot Posterior Predictive Distribution Handling of Missing Data Floating Point Errors and Overflows Handling Error Messages Computational Resources Displayed Output ODS Table Names ODS Graphics
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Examples
Simulating Samples From a Known Density Box-Cox Transformation Logistic Regression Model with a Diffuse Prior Logistic Regression Model with Jeffreys’ Prior Poisson Regression Nonlinear Poisson Regression Models Logistic Regression Random-Effects Model Nonlinear Poisson Regression Random-Effects Model Multivariate Normal Random-Effects Model Change Point Models Exponential and Weibull Survival Analysis Time Independent Cox Model Time Dependent Cox Model Piecewise Exponential Frailty Model Normal Regression with Interval Censoring Constrained Analysis Implement a New Sampling Algorithm Using a Transformation to Improve Mixing Gelman-Rubin Diagnostics
- References
Syntax: MCMC Procedure
The following statements are available in PROC MCMC. Items within < > are optional.
- PROC MCMC <options> ;
- ARRAY arrayname <{ dimensions }> ;
- BEGINCNST/ENDCNST ;
- BEGINNODATA/ENDNODATA ;
- BY variables ;
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MODEL
variable
distribution
; - PARMS parameter <=> number </options> ;
- PREDDIST <’label’> OUTPRED=SAS-data-set <options> ;
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PRIOR/HYPERPRIOR
parameter distribution
;
- Program statements ;
- RANDOM random-effects-specification ;
- 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 every Bayesian model.
In addition, you can use the ARRAY statement to define constant or parameter arrays, the BEGINCNST/ENDCNST and similar statements to save 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, and finally the UDS statements to define your own Gibbs samplers to sample any parameters in the model.
The following sections provide a description of each of these statements.