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Gaussian Markov distributions over finite graphs. (English) Zbl 0589.62033

Summary: Gaussian Markov distributions are characterized by zeros in the inverse of their covariance matrix and we describe the conditional independencies which follow from a given pattern of zeros. Describing Gaussian distributions with given marginals and solving the likelihood equations with covariance selection models both lead to a problem for which we present two cyclic algorithms.

The first generalises a published algorithm of N. Wermuth and E. Scheidt for covariance selection whilst the second is analogous to the iterative proportional scaling of contingency tables. A convergence proof is given for these algorithms and this uses the notion of I-divergence.


MSC:
62H05Characterization and structure theory (Multivariate analysis)
62F99Parametric inference
60K99Special processes
05C50Graphs and linear algebra