A tutorial on Bayes factor estimation with the product space method

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• 作者：Tom Lodewyckx^a ;   ; ^{tom.lodewyckx@psy.kuleuven.be} ; Woojae Kim^b ; Michael D. Lee^c ; Francis Tuerlinckx^a ; Peter Kuppens^a ; Eric-Jan Wagenmakers^d
• 关键词：Bayes factor ; Bayesian statistics ; Graphical modeling ; Hierarchical modeling ; Hypothesis testing ; Model selection ; Product space method ; Transdimensional MCMC
• 刊名：Journal of Mathematical Psychology
• 出版年：2011
• 出版时间：October 2011
• 年：2011
• 卷：55
• 期：5
• 页码：331-347
• 全文大小：872 K

文摘

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 (). 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.