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.
Publié le : 1994-12-14
Classification:
Posterior distributions,
Stein's identity,
martingale convergence theorem,
stopping time,
Jeffreys' prior,
reference prior,
repeated likelihood ratio tests,
62L12
@article{1176325758,
author = {Sun, Dongchu},
title = {Integrable Expansions for Posterior Distributions for a Two-Parameter Exponential Family},
journal = {Ann. Statist.},
volume = {22},
number = {1},
year = {1994},
pages = { 1808-1830},
language = {en},
url = {http://dml.mathdoc.fr/item/1176325758}
}
Sun, Dongchu. Integrable Expansions for Posterior Distributions for a Two-Parameter Exponential Family. Ann. Statist., Tome 22 (1994) no. 1, pp. 1808-1830. http://gdmltest.u-ga.fr/item/1176325758/