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March, 1986 Gaussian Markov Distributions over Finite Graphs
T. P. Speed, H. T. Kiiveri
Ann. Statist. 14(1): 138-150 (March, 1986). DOI: 10.1214/aos/1176349846


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.


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T. P. Speed. H. T. Kiiveri. "Gaussian Markov Distributions over Finite Graphs." Ann. Statist. 14 (1) 138 - 150, March, 1986.


Published: March, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0589.62033
MathSciNet: MR829559
Digital Object Identifier: 10.1214/aos/1176349846

Primary: 62F99
Secondary: 60K35

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 1 • March, 1986
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