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
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| PROC MCMC Compared with Other SAS Procedures |
PROC MCMC is unlike most other SAS/STAT procedures in that the nature of the statistical inference is Bayesian. You specify prior distributions for the parameters with PRIOR statements and the likelihood function for the data with MODEL statements. The procedure derives inferences from simulation rather than through analytic or numerical methods. You should expect slightly different answers from each run for the same problem, unless the same random number seed is used. The model specification is similar to PROC NLIN, and PROC MCMC shares much of the syntax of PROC NLMIXED.
Note that you can also carry out a Bayesian analysis with the GENMOD, PHREG, and LIFEREG procedures for generalized linear models, accelerated life failure models, Cox regression models, and piecewise constant baseline hazard models (also known as piecewise exponential models). See Chapter 39, The GENMOD Procedure, Chapter 66, The PHREG Procedure, and Chapter 50, The LIFEREG Procedure.