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August 1997 On Monte Carlo methods for estimating ratios of normalizing constants
Ming-Hui Chen, Qi-Man Shao
Ann. Statist. 25(4): 1563-1594 (August 1997). DOI: 10.1214/aos/1031594732

Abstract

Recently, estimating ratios of normalizing constants has played an important role in Bayesian computations. Applications of estimating ratios of normalizing constants arise in many aspects of Bayesian statistical inference. In this article, we present an overview and discuss the current Monte Carlo methods for estimating ratios of normalizing constants. Then we propose a new ratio importance sampling method and establish its theoretical framework. We find that the ratio importance sampling method can be better than the current methods, for example, the bridge sampling method (Meng and Wong) and the path sampling method (Gelman and Meng), in the sense of minimizing asymptotic relative mean-square errors of estimators. An example is given for illustrative purposes. Finally, we present two special applications and the general implementation issues for estimating ratios of normalizing constants.

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Ming-Hui Chen. Qi-Man Shao. "On Monte Carlo methods for estimating ratios of normalizing constants." Ann. Statist. 25 (4) 1563 - 1594, August 1997. https://doi.org/10.1214/aos/1031594732

Information

Published: August 1997
First available in Project Euclid: 9 September 2002

zbMATH: 0936.62028
MathSciNet: MR1463565
Digital Object Identifier: 10.1214/aos/1031594732

Subjects:
Primary: 62E25
Secondary: 62A15, 62A99

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 4 • August 1997
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