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August 2012 A note on Bayesian robustness for count data
Jairo A. Fúquene, Moises Delgado
Braz. J. Probab. Stat. 26(3): 279-287 (August 2012). DOI: 10.1214/10-BJPS134

Abstract

The usual Bayesian approach for count data is Gamma/Poisson conjugate analysis. However, in this conjugate analysis the influence of the prior distribution could be dominant even when prior and likelihood are in conflict. Our proposal is an analysis based on the Cauchy prior for natural parameter in exponential families. In this work, we show that the Cauchy/Poisson posterior model is a robust model for count data in contrast with the usual conjugate Bayesian approach Gamma/Poisson model. We use the polynomial tails comparison theorem given in (Bayesian Anal. 4 (2009) 817–843) that gives easy-to-check conditions to ensure prior robustness. In short, this means that when the location of the prior and the bulk of the mass of the likelihood get further apart (a situation of conflict between prior and likelihood information), Bayes theorem will cause the posterior distribution to discount the prior information. Finally, we analyze artificial data sets to investigate the robustness of the Cauchy/Poisson model.

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Jairo A. Fúquene. Moises Delgado. "A note on Bayesian robustness for count data." Braz. J. Probab. Stat. 26 (3) 279 - 287, August 2012. https://doi.org/10.1214/10-BJPS134

Information

Published: August 2012
First available in Project Euclid: 5 April 2012

zbMATH: 1239.62019
MathSciNet: MR2911706
Digital Object Identifier: 10.1214/10-BJPS134

Keywords: Cauchy/Poisson model , exponential family , polynomial tails comparison theorem , robust priors

Rights: Copyright © 2012 Brazilian Statistical Association

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Vol.26 • No. 3 • August 2012
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