JSM 2004 - Toronto

Abstract #300119

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Activity Number: 202
Type: Invited
Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #300119
Title: A General Approach for Constructing Priors for Covariance Selection Models
Author(s): Robert Kohn*+
Companies: University of New South Wales
Address: Faculty of Commerce and Economics, Sydney, International, 2052, Australia
Keywords: constrained Wishart distribution ; element selection ; graphical models ; multivariate analysis
Abstract:

We consider the Bayesian estimation of an inverse covariance matrix from Gaussian data. Methods are given to construct priors for covariance selection models where the marginal distribution of the model size has a simple form. The priors have normalizing constants for each possible model size, rather than for each possible model, which gives a tractable number of normalizing constants that we estimate using Markov chain Monte Carlo methods and store offline. Our priors do not require the restriction that the corresponding graphical models are decomposable. We illustrate our method using two examples. The first has a constrained Wishart distribution conditionally on the covariance selection model. The second example uses the prior where the inverse covariance matrix is decomposed into scale and partial correlation terms.

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