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

Digital Object Identifier
doi:10.1214/aos/1176349846

Mathematical Reviews number (MathSciNet)
MR829559

Zentralblatt MATH identifier
0589.62033

JSTOR