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December, 1994 Integrable Expansions for Posterior Distributions for a Two-Parameter Exponential Family
Dongchu Sun
Ann. Statist. 22(4): 1808-1830 (December, 1994). DOI: 10.1214/aos/1176325758


Asymptotic expansions of posterior distributions are derived for a two-dimensional exponential family, which includes normal, gamma, inverse gamma and inverse Gaussian distributions. Reparameterization allows us to use a data-dependent transformation, convert the likelihood function to the two-dimensional standard normal density and apply a version of Stein's identity to assess the posterior distributions. Applications are given to characterize optimal noninformative priors in the sense of Stein, to suggest the form of a high-order correction to the distribution function of a sequential likelihood ratio statistic and to provide confidence intervals for one parameter in the presence of other nuisance parameters.


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Dongchu Sun. "Integrable Expansions for Posterior Distributions for a Two-Parameter Exponential Family." Ann. Statist. 22 (4) 1808 - 1830, December, 1994.


Published: December, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0828.62071
MathSciNet: MR1329169
Digital Object Identifier: 10.1214/aos/1176325758

Primary: 62L12

Keywords: Jeffreys' prior , martingale convergence theorem , posterior distributions , reference prior , repeated likelihood ratio tests , Stein's identity , stopping time

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 4 • December, 1994
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