Gaussian Markov distributions over finite graphs.

*(English)*Zbl 0589.62033Summary: 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:

62H05 | Characterization and structure theory (Multivariate analysis) |

62F99 | Parametric inference |

60K99 | Special processes |

05C50 | Graphs and linear algebra |