SAS/STAT software provides Bayesian capabilities in six procedures: BCHOICE, FMM, GENMOD, LIFEREG, MCMC, and PHREG. The FMM, GENMOD, LIFEREG, and PHREG procedures provide Bayesian analysis in addition to the standard frequentist analyses 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 MCMC procedure is a general procedure that fits Bayesian models with arbitrary priors and likelihood functions.

This chapter provides an overview of Bayesian statistics; describes specific sampling algorithms used in these four 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 27: The BCHOICE Procedure), FMM (see Chapter 39: The FMM Procedure), GENMOD (see Chapter 44: The GENMOD Procedure), LIFEREG (see Chapter 69: The LIFEREG Procedure), MCMC (see Chapter 73: The MCMC Procedure), and PHREG (see Chapter 85: The PHREG Procedure).