Bayes factors for nonlinear hypotheses and likelihood distributions

Robert McCulloch, Peter E. Rossi

Research output: Contribution to journalArticle

27 Citations (Scopus)

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 1992
Externally publishedYes

Fingerprint

Bayes Factor
Logistics
Likelihood
Prior distribution
Restricted Parameter Space
Kullback-Leibler Divergence
Distance Metric
disease diagnosis
Logistic Regression
Marginal Distribution
Projection Method
Diagnostics
Logistic Models
methodology
Projection
Restriction
Metric
Bayes factor

Keywords

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

ASJC Scopus subject areas

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

Cite this

Bayes factors for nonlinear hypotheses and likelihood distributions. / McCulloch, Robert; Rossi, Peter E.

In: Biometrika, Vol. 79, No. 4, 12.1992, p. 663-676.

Research output: Contribution to journalArticle

McCulloch, Robert ; Rossi, Peter E. / Bayes factors for nonlinear hypotheses and likelihood distributions. In: Biometrika. 1992 ; Vol. 79, No. 4. pp. 663-676.
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