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December 2013 Bayesian Estimation of the Discrepancy with Misspecified Parametric Models
Pierpaolo De Blasi, Stephen G. Walker
Bayesian Anal. 8(4): 781-800 (December 2013). DOI: 10.1214/13-BA024

Abstract

We study a Bayesian model where we have made specific requests about the parameter values to be estimated. The aim is to find the parameter of a parametric family which minimizes a distance to the data generating density and then to estimate the discrepancy using nonparametric methods. We illustrate how coherent updating can proceed given that the standard Bayesian posterior from an unidentifiable model is inappropriate. Our updating is performed using Markov Chain Monte Carlo methods and in particular a novel method for dealing with intractable normalizing constants is required. Illustrations using synthetic data are provided.

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Pierpaolo De Blasi. Stephen G. Walker. "Bayesian Estimation of the Discrepancy with Misspecified Parametric Models." Bayesian Anal. 8 (4) 781 - 800, December 2013. https://doi.org/10.1214/13-BA024

Information

Published: December 2013
First available in Project Euclid: 4 December 2013

zbMATH: 1329.62123
MathSciNet: MR3150469
Digital Object Identifier: 10.1214/13-BA024

Keywords: asymptotics , Bayesian nonparametrics , Gaussian process , Kullback–Leibler divergence , posterior consistency , Semi–parametric density model

Rights: Copyright © 2013 International Society for Bayesian Analysis

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Vol.8 • No. 4 • December 2013
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