JSM 2005 - Toronto

Abstract #302422

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 211
Type: Invited
Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #302422
Title: A New Class of Conjugate Priors for Decomposable Graphical Gaussian Models
Author(s): Helene M. Massam*+ and Gerald Letac
Companies: York University and Universite Paul Sabatier
Address: 4700 Keele Street, Toronto, ON, M3J 1P3, Canada
Keywords: conjugate prior ; graphical Gaussian model ; hyper Markov ; homogeneous graph ; exponential family
Abstract:

In this paper, we present a new class of conjugate prior distributions for the covariance parameter of graphical Gaussian models Markov with respect to a decomposable graph G. This new class comprises the Diaconis-Ylvisaker conjugate prior, the G-Wishart, which is the inverse of the hyper inverse Wishart as defined by Dawid and Lauritzen (1993). It also comprises the Wisharts defined by Andersson and Wojnar (2004) Markov with respect to a homogeneous graph (i.e., a decomposable graph that does not have the three-link chain as an induced subgraph). This new class of priors is richer than the G-Wishart because its shape parameter set is of a dimension at least equal to the number of cliques plus one. It is richer than homogeneous Wisharts because it is valid for any decomposable G. It is not strong hyper Markov like the two special families mentioned above, but it is weak hyper Markov---the strongest Markov property that can be expected given its generality. This family is generated as an exponential family.

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