Abstract
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.
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G.C.’s research was partially supported by MIUR, Rome, (PRIN 2003138887) and the University of Pavia. P.V.’s research was partially supported by MIUR, Rome, (PRIN 2003138887) and by L. Bocconi University. The research of E.G. was partially supported by CONACyT (Grant 32256-E) and SNI, Mexico. The authors also benefited from partial support through Project No. 4 of the Bilateral Executive Programme for Technological and Scientific Co-operation Between Italy and Mexico 2003–2005.
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Consonni, G., Gutiérrez-Peña, E. & Veronese, P. Compatible priors for Bayesian model comparison with an application to the Hardy–Weinberg equilibrium model. TEST 17, 585–605 (2008). https://doi.org/10.1007/s11749-007-0057-7
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DOI: https://doi.org/10.1007/s11749-007-0057-7
Keywords
- Bayes factor
- Conjugate prior
- Dirichlet distribution
- Jeffreys conditioning
- Kullback–Leibler projection
- Nested model
- Predictive distribution
- Trinomial distribution