Going Beyond Convergence in Bayesian Estimation: Why Precision Matters Too and How to Assess It. Issue 4 (4th July 2019) - Zitzmann, Steffen; Hecht, Martin
Abstract : Most of the software that is available to implement Bayesian approaches uses Markov chain Monte Carlo (MCMC) methods. It is our impression that many researchers are primarily concerned with convergence as assessed by the Potential Scale Reduction (PSR) and that other aspects of MCMC are largely ignored. In this article, we argue that the precision with which the Bayesian estimates are approximated by summary statistics for the MCMC chain is essential to ensure good statistical properties. We discuss the Effective Sample Size (ESS), which indicates how well an estimate is approximated, and present evidence from two simulation studies and an example from organizational research to support our claim that researchers should be concerned not only with convergence but also with precision, particularly when a multilevel model is estimated. In addition, we demonstrate how M plus can be modified so that users can control the ESS, and we conclude with recommendations.