JSM 2004 - Toronto

Abstract #300830

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Activity Number: 436
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #300830
Title: Optimality of Median Probability Model in Generalized Linear Models
Author(s): Samiran Ghosh*+ and Dipak K. Dey
Companies: University of Connecticut and University of Connecticut
Address: 215 Glennbrook Rd., U-4120, Storrs, CT, 06269,
Keywords: Bayes factor ; deviance loss ; Poisson regression ; binomial regression ; GLM ; predictive distribution
Abstract:

Goal of optimal model selection is of two fold. First select a model which fits the data well and second use selected model for future prediction. Under Bayesian philosophy it is commonly perceived that the optimal predictive model is the model with highest posterior probability. Recently Berger and Barberi (2003) have shown that for linear models with normal error structure, median probability model is the optimal predictive model which often differs from highest probability model. We have investigated their findings in generalized linear model (GLM). First, we have developed some optimality conditions for GLM, which will generalize the optimality theory of median probability model. In particular we have considered Binomial and Poisson case in much detail. Finally real data examples are used to illustrate the proposed methodology.

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Revised March 2004