Abstract #300459

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JSM 2002 Abstract #300459
Activity Number: 147
Type: Contributed
Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Stat. Sciences*
Abstract - #300459
Title: Using Differential Geometry to Study Robustness in Bayesian Statistics
Author(s): Marvin Gruber*+
Affiliation(s): Rochester Institute of Technology
Address: 85 Lomb Memorial Drive, Rochester, New York, 14623, United States of America
Keywords: geodesic ; Kalman filter ; robustness of prior distributions ; asymptotic results ; robustness
Abstract:

An important problem in Bayesian statistics is how the choice of prior distributions influence inferences. One way to study this is to compare values of measures of distance between prior and posterior distributions for different sample sizes and parameter values. The geodesic distance between probability distributions originally proposed by C.R.Rao is one such measure. Using formulae for the geodesic distances between probability distributions, the distances between posterior distributions are obtained for different kinds of prior distributions. These include normal, beta, and the exponential priors for normal Poisson--exponential and Weibull and binomial populations. Illustrations will be given in the context of reliability and for the Kalman filter. Some asymptotic results about these distances will be derived.

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