I examine philosophical problems and sampling deficiencies associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes methodology. Because the prior densities used to define alternative hypotheses in many Bayesian tests assign non-negligible probability
to regions of the parameter space that are consistent with null
hypotheses, resulting tests provide exponential accumulation of
evidence in favour of true alternative hypotheses, but only sub-linear
accumulation of evidence in favour of true null hypotheses. Thus, it
is often impossible for such tests to provide strong evidence in favour
of a true null hypothesis, even when moderately large sample sizes have
been obtained. Because Bayesian hypothesis tests yield probability
statements regarding the truth of the null hypothesis (rather than a
frequentist decision to simply not reject the hypothesis), this imbalance
in the rates of accumulation of evidence is problematic.
After reviewing asymptotic convergence rates of Bayes factors for
testing precise null hypotheses, I will propose two new classes of prior
densities that ameliorate the imbalance in convergence rates inherited by
most Bayesian tests. Using members of these classes, I obtain analytic
expressions for Bayes factors in linear models and derive approximations
to Bayes factors in large-sample settings. Examples illustrating the
application of these tests will be discussed.
Meet the speaker in Room 212 Cockins Hall at 4:30
p.m. Refreshments will be served.
