The Annals of Statistics

On convergence of posterior distributions

Subhashis Ghosal, Jayanta K. Ghosh, and Tapas Samanta

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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.

Article information

Ann. Statist., Volume 23, Number 6 (1995), 2145-2152.

First available in Project Euclid: 15 October 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference 62F25: Tolerance and confidence regions

Asymptotics Bernstein-von Mises theorem Bayes estimates convergence of posterior likelihood ratio process


Ghosal, Subhashis; Ghosh, Jayanta K.; Samanta, Tapas. On convergence of posterior distributions. Ann. Statist. 23 (1995), no. 6, 2145--2152. doi:10.1214/aos/1034713651.

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