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December 2010 A Bayesian Edgeworth expansion by Stein's identity
Ruby C. Weng
Bayesian Anal. 5(4): 741-763 (December 2010). DOI: 10.1214/10-BA526

Abstract

The Edgeworth expansion is a series that approximates a probability distribution in terms of its cumulants. One can derive it by first expanding the probability distribution in Hermite orthogonal functions and then collecting terms in powers of the sample size. This paper derives an expansion for posterior distributions which possesses these features of an Edgeworth series. The techniques used are a version of Stein's Identity and properties of Hermite polynomials. Two examples are provided to illustrate the accuracy of our series.

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Ruby C. Weng. "A Bayesian Edgeworth expansion by Stein's identity." Bayesian Anal. 5 (4) 741 - 763, December 2010. https://doi.org/10.1214/10-BA526

Information

Published: December 2010
First available in Project Euclid: 19 June 2012

zbMATH: 1330.62084
MathSciNet: MR2740155
Digital Object Identifier: 10.1214/10-BA526

Keywords: Edgeworth expansion , Hermite polynomials , Laplace method , marginal posterior distribution , Stein's identity

Rights: Copyright © 2010 International Society for Bayesian Analysis

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Vol.5 • No. 4 • December 2010
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