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Frequentist Validity of Posterior Quantiles for a Two-Parameter Exponential Family

Dongchu Sun and Keying Ye
Biometrika
Vol. 83, No. 1 (Mar., 1996), pp. 55-65
Published by: Oxford University Press on behalf of Biometrika Trust
Stable URL: http://www.jstor.org/stable/2337432
Page Count: 11
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Frequentist Validity of Posterior Quantiles for a Two-Parameter Exponential Family
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Abstract

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.

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