JSM 2004 - Toronto

Abstract #301054

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Activity Number: 414
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract - #301054
Title: The Use of Kullback-Leibler Divergences in Bayesian Sensitivity Analysis
Author(s): Daniel M. Farewell*+
Companies: Lancaster University
Address: Dept. of Mathematics and Statistics, Lancaster, International, LA1 4YF, England
Keywords: Bayesian sensitivity analysis ; Kullback-Leibler divergence
Abstract:

Model checking or "criticism" is an important aspect of statistics, and for the Bayesian statistician it falls neatly into two categories: the criticism of the choice of likelihood and the criticism of the prior distribution(s). This talk examines a technique proposed by Anthony O'Hagan in Highly Structured Stochastic Systems (2003) for criticizing the choices of prior. In order to criticize the choice of prior for a parameter p, the Kullback-Leibler divergence between the (marginal) prior and posterior distributions for p is estimated, approximating the information gained about p from the data. The scale and interpretation of the K-L divergence will be discussed. Estimation is briefly considered, and an unbiased estimate (which could be routinely implemented in computer packages such as WinBUGS) is proposed. While simple to estimate, the Kullback-Leibler divergence is difficult to interpret and thus methodology for an automated "red flag" signaling posterior sensitivity to the choice of priors remains an area for future research.

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