Premium
Properties of Bayes Factors Based on Test Statistics
Author(s) -
JOHNSON VALEN E.
Publication year - 2008
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2007.00576.x
Subject(s) - bayes factor , bayes' theorem , statistics , mathematics , bayes' rule , bayes error rate , dirichlet distribution , multinomial distribution , bayesian statistics , hyperparameter , statistical hypothesis testing , bayesian probability , econometrics , bayes classifier , bayesian inference , algorithm , mathematical analysis , boundary value problem
. This article examines the consistency, interpretation and application of Bayes factors constructed from standard test statistics. Primary conclusions are that Bayes factors based on multinomial and normal test statistics are consistent for suitable choices of the hyperparameters used to specify alternative hypotheses, and that such constructions can be extended to obtain consistent Bayes factors based on likelihood ratio statistics. A connection between Bayes factors based on likelihood ratio statistics and the Bayesian information criterion is exposed, as is a connection between Bayes factors based on F statistics and parametric Bayes factors based on normal‐inverse gamma models. Similarly, Bayes factors based on chi‐squared statistics for multinomial data are shown to provide accurate approximations to Bayes factors based on multinomial/Dirichlet models. An illustration of how the simple form of these Bayes factors can be exploited to generate easily interpretable summaries of the experimental ‘weight of evidence’ is provided.