The Number of MCMC Draws Needed to Compute Bayesian Credible Bounds

In the past 20 years, there has been a staggering increase in the use of Bayesian statistical inference, based on Markov chain Monte Carlo (MCMC) methods, to estimate model parameters and other quantities of interest. This trend exists in virtually all areas of engineering and science. In a typical application, researchers will report estimates of parametric functions (e.g., quantiles, probabilities, or predictions of future outcomes) and corresponding intervals from MCMC methods. One difficulty with the use of inferential methods based on Monte Carlo (MC) is that reported results may be inaccurate due to MC error. MC error, however, can be made arbitrarily small by increasing the number of MC draws. Most users of MCMC methods seem to use indirect diagnostics, trial-and-error, or guess-work to decide how long to run a MCMC algorithm and accuracy of MCMC output results is rarely reported. Unless careful analysis is done, reported numerical results may contain digits that are completely meaningless. In this article, we describe an algorithm to provide direct guidance on the number of MCMC draws needed to achieve a desired amount of precision (i.e., a specified number of accurate significant digits) for Bayesian credible interval endpoints.