Bayes factor biases for non‐nested models and corrections

Abstract

AbstractWith the advent of simulation‐based methods to obtain samples from posteriors and due to increases in computational power, Bayesian methods are increasingly applied to complex problems, sometimes providing the only available methods where likelihood implementations are difficult. As a consequence a large body of research in science and social science increasingly utilizes Bayesian tools, often applying them with default settings. A fundamental problem of interest is model selection, and Bayes factors provide a natural approach to Bayesian model selection. Using Laplace approximations and illustrative examples we demonstrate that Bayes factors can have strong biases toward particular models even in non‐nested settings with the same number of parameters. Several easily implemented corrections are shown to provide effective cross‐checks to default Bayes Factors. The Canadian Journal of Statistics 45: 290–309; 2017 © 2017 Statistical Society of Canada