A Bayesian approach is used to estimate the covariance matrix of Gaussiandata. Ideas from Gaussian graphical models and model selection are used toconstruct a prior for the covariance matrix that is a mixture over alldecomposable graphs. For this prior the probability of each graph size isspecified by the user and graphs of equal size are assigned equal probability.Most previous approaches assume that all graphs are equally probable. We showempirically that the prior that assigns equal probability over graph sizesoutperforms the prior that assigns equal probability over all graphs, both inidentifying the correct decomposable graph and in more efficiently estimatingthe covariance matrix.
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