Testing Hardy-Weinberg equilibrium: an objective Bayesian analysis

Abstract

We analyze the general (multiallelic) Hardy-Weinberg equilibrium problem from an objective Bayesian testing standpoint. We argue that for small or moderate sample sizes the answer is rather sensitive to the prior chosen, and this suggests to carry out a sensitivity analysis with respect to the prior. This goal is achieved through the identification of a class of priors specifically designed for this testing problem. In this paper, we consider the class of intrinsic priors under the full model, indexed by a tuning quantity, the training sample size. These priors are objective, satisfy Savage's continuity condition and have proved to behave extremely well for many statistical testing problems. We compute the posterior probability of the Hardy-Weinberg equilibrium model for the class of intrinsic priors, assess robustness over the range of plausible answers, as well as stability of the decision in favor of either hypothesis.