On the uniqueness of probability matching priors

A-M Staicu, Nancy Reid

Research output: Working paperWorking paper and Preprints

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Abstract

Probability matching priors are priors for which Bayesian and frequentist inference, in the form of posterior quantiles, or confidence intervals, agree to some order of approximation. These priors are constructed by solving a first order partial differential equation, that may be difficult to solve. However, Peers (1965) and Tibshirani (1989) showed that under parameter orthogonality a family of matching priors can be obtained. The present work shows that, when used in a third order approximation to the posterior marginal density, the Peers-Tibshirani class of matching priors is essentially unique.
Original languageEnglish
Publication statusPublished - 2007

Bibliographical note

Sponsorship: NSERC

Keywords

  • orthogonal parameters
  • approximate Bayesian inference
  • Laplace approximation
  • tail probability approximation

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