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June 2016 Expert Information and Nonparametric Bayesian Inference of Rare Events
Hwan-sik Choi
Bayesian Anal. 11(2): 421-445 (June 2016). DOI: 10.1214/15-BA956

Abstract

Prior distributions are important in Bayesian inference of rare events because historical data information is scarce, and experts are an important source of information for elicitation of a prior distribution. I propose a method to incorporate expert information into nonparametric Bayesian inference on rare events when expert knowledge is elicited as moment conditions on a finite dimensional parameter θ only. I generalize the Dirichlet process mixture model to merge expert information into the Dirichlet process (DP) prior to satisfy expert’s moment conditions. Among all the priors that comply with expert knowledge, we use the one that is closest to the original DP prior in the Kullback–Leibler information criterion. The resulting prior distribution is given by exponentially tilting the DP prior along θ. I provide a Metropolis–Hastings algorithm to implement this approach to sample from posterior distributions with exponentially tilted DP priors. The proposed method combines prior information from a statistician and an expert by finding the least-informative prior given expert information.

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Hwan-sik Choi. "Expert Information and Nonparametric Bayesian Inference of Rare Events." Bayesian Anal. 11 (2) 421 - 445, June 2016. https://doi.org/10.1214/15-BA956

Information

Published: June 2016
First available in Project Euclid: 26 May 2015

zbMATH: 1357.62152
MathSciNet: MR3471997
Digital Object Identifier: 10.1214/15-BA956

Keywords: defaults , Dirichlet process mixture , Kullback–Leibler information criterion , maximum entropy , Metropolis–Hastings algorithm

Rights: Copyright © 2016 International Society for Bayesian Analysis

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Vol.11 • No. 2 • June 2016
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