The Annals of Statistics

Gaussian Markov Distributions over Finite Graphs

T. P. Speed and H. T. Kiiveri

Full-text: Open access

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

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176349846

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176349846

Mathematical Reviews number (MathSciNet)
MR829559

Zentralblatt MATH identifier
0589.62033

Subjects
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]

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

Citation

Speed, T. P.; Kiiveri, H. T. Gaussian Markov Distributions over Finite Graphs. The Annals of Statistics 14 (1986), no. 1, 138--150. doi:10.1214/aos/1176349846. http://projecteuclid.org/euclid.aos/1176349846.


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