Abstract

In what follows I will discuss an example of the Duhem-Quine problem in which Pr(H A), Pr(A H), and Pr(OI +H& ?A) (where H is the hypothesis, A the auxiliary assumptions, and O the observational prediction) can be construed objectively; however, only some of those quantities are relevant to the analysis that I provide. The example involves medical diagnosis. The goal is to test the hypothesis that someone has tuberculosis; the auxiliary assumptions describe the er- ror characteristics of the test procedure. Although it can make sense to talk about the objective probability that someone (randomly drawn from a given population) has tuberculosis and it also can make sense to talk about the objective probability that a test procedure has a certain set of error characteristics, neither of these quantities will enter into the analysis. The analysis proceeds entirely via likelihoods, what one needs to consider is just the probability of the observations conditional on four conjunctions of the form (?H & +A).' It is a special feature of the example that all four of these conjunctions are simple statistical hypotheses in the technical sense that each unambigu-ously confers a probability on the observations.'o After describing how the likelihood concept applies to the example concerning medical diagnosis, I will show how similar patterns can arise in the context of a second inferential framework-that of H. Akaike's criterion of model selection;" this time the example will involve phylogenetic inference.