Bayes factors for nonlinear hypotheses and likelihood distributions

Robert E. Mcculloch, Peter E. Rossi

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

SUMMARY: New methods are proposed which allow Bayes factors to be computed for hypotheses which impose nonlinear restrictions on the parameters. Projection methods are used to induce the prior distribution over the restricted parameter space which is required for computation of the Bayes factor. Various distance metrics are introduced to define the projection, including a utility-based metric which gives Kullback-Leibler divergence as a special case. Draws from the restricted and unrestricted prior distributions are used to construct marginal distributions of the likelihood which is shown to have additional diagnostic value over and above the Bayes factor. These methods are applied to hypotheses in logistic regression.

Original languageEnglish (US)
Pages (from-to)663-676
Number of pages14
JournalBiometrika
Volume79
Issue number4
DOIs
StatePublished - Dec 1 1992
Externally publishedYes

Keywords

  • Bayes Factor
  • Kullback-Leibler divergence
  • Logistic regression
  • Nonlinear modelNonlinear hypothesis

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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