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On Convergence of Posterior Distributions
Subhashis Ghosal, Jayanta K. Ghosh and Tapas Samanta
The Annals of Statistics
Vol. 23, No. 6 (Dec., 1995), pp. 2145-2152
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2242789
Page Count: 8
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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.
The Annals of Statistics © 1995 Institute of Mathematical Statistics