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TEST

, Volume 17, Issue 3, pp 585–605 | Cite as

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

  • Guido Consonni
  • Eduardo Gutiérrez-PeñaEmail author
  • Piero Veronese
Original Paper

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.

Keywords

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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Copyright information

© Sociedad de Estadística e Investigación Operativa 2007

Authors and Affiliations

  • Guido Consonni
    • 1
  • Eduardo Gutiérrez-Peña
    • 2
    Email author
  • Piero Veronese
    • 3
  1. 1.Università di PaviaPaviaItaly
  2. 2.IIMAS, Universidad Nacional Autónoma de MéxicoMexico D.F.Mexico
  3. 3.Università L. BocconiMilanoItaly

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