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Biometrika 1996 83(1):55-65; doi:10.1093/biomet/83.1.55
© 1996 by Biometrika Trust
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Frequentist validity of posterior quantiles for a two-parameter exponential family

DONGCHU SUN and KEYING YE

Department of Statistics, University of Missouri-Columbia Columbia, Missouri 65211, U.S.A.
Department of Statistics, Virginia Polytechnic Institute and State University Blacksbury, Virginia 24061-0439, U.S.A.

Berger & Bernardo's (1989) reference priors and Tibshirani (1989) priors are derived for distributions in Bar-Lev & Reiser's (1982) two-parameter exponential family when either the location or the scale parameter is of interest. The reference prior is shown to be a Tibshirani prior. Furthermore, conditions under which a Tibshirani prior is a higher-order matching prior are investigated. When both the parameters are of interest, it is also shown that the reference prior agrees with the prior matching the posterior and frequentist expansions based on the signed square root of log-likelihood ratio. The normal, inverse Gaussian, and gamma distributions are used to illustrate the results.

Key Words: Gamma distribution • Inverse Gaussian distribution • Matching prior, Normal distribution • Orthogonal parametrisation • Reference prior • Signed log-likelihood ratio


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