## The Annals of Statistics

### Gaussian Markov Distributions over Finite Graphs

#### Abstract

Gaussian Markov distributions are characterised 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 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.

#### Article information

Source
Ann. Statist. Volume 14, Number 1 (1986), 138-150.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176349846

JSTOR