A SAS Macro for Automated Stopping of Markov Chain Monte Carlo Estimation in Bayesian Modeling with PROC MCMC

Abstract

A crucial challenge in Bayesian modeling using Markov chain Monte Carlo (MCMC) estimation is to diagnose the convergence of the chains so that the draws can be expected to closely approximate the posterior distribution on which inference is based. A close approximation guarantees that the MCMC error exhibits only a negligible impact on model estimates and inferences. However, determining whether convergence has been achieved can often be challenging and cumbersome when relying solely on inspecting the trace plots of the chain(s) or manually checking the stopping criteria. In this article, we present a SAS macro called %automcmc that is based on PROC MCMC and that automatically continues to add draws until a user-specified stopping criterion (i.e., a certain potential scale reduction and/or a certain effective sample size) is reached for the chain(s).

Keywords

• Bayesian statistics
• Markov chain Monte Carlo
• SAS
• PROC MCMC