Compatible priors for Bayesian model comparison with an application to the Hardy-Weinberg equilibrium model

Suppose we entertain Bayesian inference under a collection of models. This requires assigning a corresponding collection of prior distributions, one for each model's parameter space. In this paper we address the issue of relating priors across models, and provide both a conceptual and a pragmatic justification for this task. Specifically, we consider the notion of "compatible" priors across models, and discuss and compare several strategies to construct such distributions. To explicate the issues involved, we refer to a specific problem, namely, testing the Hardy-Weinberg Equilibrium model, for which we provide a detailed analysis using Bayes factors.