Abstract

Allan Birnbaum has alleged that use of a likelihood criterion can find strong evidence against a true hypothesis with probability one. It is shown that, correctly applied, use of the likelihood function does not lead to any such result. Specifically, Birnbaum's example involves composite hypotheses, and, from a Bayesian point of view, the support of a composite hypothesis can be adequately assessed only by averaging the likelihoods of its constituent simple hypotheses.