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.
Bayes factor Conjugate prior Dirichlet distribution Jeffreys conditioning Kullback–Leibler projection Nested model Predictive distribution Trinomial distribution
Mathematics Subject Classification (2000)
62F15 62P10 92D25
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Dawid AP, Lauritzen SL (2001) Compatible prior distributions. In: George E (ed) Bayesian methods with applications to science, policy and official statistics. Monographs of official statistics Office for official publications of the European Communities, Luxembourg, pp 109–118. http://www.stat.cmu.edu/ISBA/index.html