Physical Sciences and Mathematics Commons^™

A Remarkably Simple And Accurate Method For Computing The Bayes Factor From A Markov Chain Monte Carlo Simulation Of The Posterior Distribution In High Dimension, Martin D. Weinberg, Ilsang Yoon, Neal S. Katz

Neal S. Katz

Weinberg (2012) described a constructive algorithm for computing the marginal likelihood, Z, from a Markov chain simulation of the posterior distribution. Its key point is: the choice of an integration subdomain that eliminates subvolumes with poor sampling owing to low tail-values of posterior probability. Conversely, this same idea may be used to choose the subdomain that optimizes the accuracy of Z. Here, we explore using the simulated distribution to define a small region of high posterior probability, followed by a numerical integration of the sample in the selected region using the volume tessellation algorithm described inWeinberg (2012). Even more promising …