Title: On the Ubiquity of Information Inconsistency for Conjugate Priors,
Abstract: Informally, "Information Inconsistency" is the property that has been
observed in many Bayesian hypothesis testing and model selection procedures
whereby the Bayesian conclusion does not become definitive when the data seems
to become definitive. An example is that, when performing a t-test using
standard conjugate priors, the Bayes factor of the alternative hypothesis to
the null hypothesis remains bounded as the t statistic grows to infinity. This
paper shows that information inconsistency is ubiquitous in Bayesian hypothesis
testing under conjugate priors. Yet the title does not fully describe the
paper, since we also show that theoretically recommended priors, including
scale mixtures of conjugate priors and adaptive priors, are information
consistent. Hence the paper is simply a forceful warning that use of conjugate
priors in testing and model selection is highly problematical, and should be
replaced by the information consistent alternatives.