Z.A general (asymptotic) theory of estimation was developed by Ibragimov and Has’minskii under certain conditions on the normalized likelihood ratios. In an earlier work, the present authors studied the limiting
behaviour of the posterior distributions under the general setup of Ibragimov and Has’minskii. In particular, they obtained a necessary condition for the convergence of a suitably centered (and normalized) posterior to a constant limit in terms of the limiting likelihood ratio process. In this paper, it is shown that this condition is also sufficient to imply the posterior convergence. Some related results are also presented.
Publié le : 1995-12-14
Classification:
Asymptotics,
Bernstein-von Mises theorem,
Bayes estimates,
convergence of posterior,
likelihood ratio process,
62F15,
62F25
@article{1034713651,
author = {Ghosal, Subhashis and Ghosh, Jayanta K. and Samanta, Tapas},
title = {On convergence of posterior distributions},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 2145-2152},
language = {en},
url = {http://dml.mathdoc.fr/item/1034713651}
}
Ghosal, Subhashis; Ghosh, Jayanta K.; Samanta, Tapas. On convergence of posterior distributions. Ann. Statist., Tome 23 (1995) no. 6, pp. 2145-2152. http://gdmltest.u-ga.fr/item/1034713651/