SAS/STAT software provides Bayesian capabilities in seven procedures: BCHOICE, BGLIMM, FMM, GENMOD, LIFEREG, MCMC, and PHREG. The FMM, GENMOD, LIFEREG, and PHREG procedures provide Bayesian analysis in addition to the standard frequentist analyses that they have always performed. Thus, these procedures provide convenient access to Bayesian modeling and inference for finite mixture models, generalized linear models, accelerated life failure models, Cox regression models, and piecewise constant baseline hazard models (also known as piecewise exponential models). The BCHOICE procedure provides Bayesian analysis for discrete choice models. The BGLIMM procedure performs Bayesian analysis for generalized linear mixed-effects models (GLMMs). The MCMC procedure is a general procedure that fits a wide-range of Bayesian models that can contain, for example, arbitrary priors and likelihood functions.
This chapter provides an overview of Bayesian statistics; describes specific sampling algorithms used in these procedures; and discusses posterior inference and convergence diagnostics computations. Sources that provide in-depth treatment of Bayesian statistics can be found at the end of this chapter, in the section A Bayesian Reading List. Additional chapters contain syntax, details, and examples for the individual procedures BCHOICE (see Chapter 30, The BCHOICE Procedure), BGLIMM (see Chapter 31, The BGLIMM Procedure), FMM (see Chapter 46, The FMM Procedure), GENMOD (see Chapter 51, The GENMOD Procedure), LIFEREG (see Chapter 76, The LIFEREG Procedure), MCMC (see Chapter 80, The MCMC Procedure), and PHREG (see Chapter 92, The PHREG Procedure).