The Annals of Statistics

On convergence of posterior distributions

Subhashis Ghosal, Jayanta K. Ghosh, and Tapas Samanta

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 15 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1034713651

Digital Object Identifier
doi:10.1214/aos/1034713651

Mathematical Reviews number (MathSciNet)
MR1389869

Zentralblatt MATH identifier
0858.62024

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1034713651


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References

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