Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models

2007/06/09 by Helen Armstrong, Christopher K. Carter, Armstrong, Helen +5 · 1 citation
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #stat.ME

paper · pdf · doi:10.48550/arxiv.0706.1287

28 pages and 11 figures

arxiv created 2007/06/09 · arxiv updated 2009/12/01

Abstract

A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs. For this prior the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. Most previous approaches assume that all graphs are equally probable. We show empirically that the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both in identifying the correct decomposable graph and in more efficiently estimating the covariance matrix.

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