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Abstract:
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Most objective Bayesian hypothesis tests result in exponential accumulation of evidence in favor of true alternative hypotheses, but only sublinear accumulation of evidence in favor of true point null hypotheses. Thus, it is often impossible for such tests to provide strong evidence in favor of a true null hypothesis, even when moderately large sample sizes have been obtained. In this article, I review asymptotic convergence rates of standard objective Bayes factors and propose two new classes of prior densities that ameliorate the imbalance in convergence rates inherited by standard objective methods. Using members of these classes, we obtain analytic expressions for Bayes factors in linear models and derive approximations to the resulting Bayes factors in large-sample settings.
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