The Annals of Statistics

Gaussian Markov Distributions over Finite Graphs

T. P. Speed and H. T. Kiiveri

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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

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

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F99: None of the above, but in this section
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Conditional independence Markov property simple graph covariance selection $I$-divergence geometry


Speed, T. P.; Kiiveri, H. T. Gaussian Markov Distributions over Finite Graphs. Ann. Statist. 14 (1986), no. 1, 138--150. doi:10.1214/aos/1176349846.

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