JSM 2004 - Toronto

Abstract #301048

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Activity Number: 74
Type: Topic Contributed
Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract - #301048
Title: Semi-automatic Informative Priors via the Relationship between the Power Prior and Hierarchical Models
Author(s): Ming-Hui Chen*+ and Joseph G. Ibrahim
Companies: University of Connecticut and University of North Carolina, Chapel Hill
Address: Dept. of Statistics, Storrs, CT, 06269-4120,
Keywords: generalized linear model ; historical data ; power prior ; prior elicitation ; random effects model
Abstract:

The power prior has emerged as a useful informative prior for the incorporation of historical data in a Bayesian analysis. We examine formal analytical relationships between the power prior and hierarchical models, and show that the hierarchical models used for combining several datasets are a special case of the power prior. We establish these results for the normal linear model as well as for the class of generalized linear models. These analytical relationships are quite novel as they unify the theory of the power prior, demonstrate the generality of the power prior, shed new light on benchmark analyses using the power prior, and provide key insights to the estimation of the power parameter in the power prior. Several key theorems are presented establishing these formal connections, as well as a formal methodology for estimating a guide value for the power parameter. Several examples are given to illustrate the proposed methodology.

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