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Keywords:

Science & Technology, Social Sciences, Physical Sciences, Mathematics, Interdisciplinary Applications, Social Sciences, Mathematical Methods, Psychology, Mathematical, Mathematics, Mathematical Methods In Social Sciences, Psychology, Bayes factor, Bayesian statistics, Graphical modeling, Hierarchical modeling, Hypothesis testing, Model selection, Product space method, Transdimensional MCMC, IMPLICIT MEMORY TASKS, MONTE-CARLO METHODS, MODEL SELECTION, SIGNAL-DETECTION, NULL HYPOTHESIS, T TESTS, MECHANISMS, INFERENCE, BIAS, APPROXIMATIONS, 0102 Applied Mathematics, 1701 Psychology, 1702 Cognitive Sciences, Experimental Psychology, 4901 Applied mathematics, 5204 Cognitive and computational psychology

Abstract:

The Bayes factor is an intuitive and principled model selection tool from Bayesian statistics. The Bayes factor quantifies the relative likelihood of the observed data under two competing models, and as such, it measures the evidence that the data provides for one model versus the other. Unfortunately, computation of the Bayes factor often requires sampling-based procedures that are not trivial to implement. In this tutorial, we explain and illustrate the use of one such procedure, known as the product space method (Carlin & Chib, 1995). This is a transdimensional Markov chain Monte Carlo method requiring the construction of a "supermodel" encompassing the models under consideration. A model index measures the proportion of times that either model is visited to account for the observed data. This proportion can then be transformed to yield a Bayes factor. We discuss the theory behind the product space method and illustrate, by means of applied examples from psychological research, how the method can be implemented in practice. © 2011 Elsevier Inc.