Model selection for Gaussian concentration graphs

Mathias Drton, Michael D. Perlman

Research output: Contribution to journalArticlepeer-review

115 Scopus citations

Abstract

A multivariate Gaussian graphical Markov model for an undirected graph G, also called a covariance selection model or concentration graph model, is defined in terms of the Markov properties, i.e. conditional independences associated with G, which in turn are equivalent to specified zeros among the set of pairwise partial correlation coefficients. By means of Fisher's z-transformation and Šidák's correlation inequality, conservative simultaneous confidence intervals for the entire set of partial correlations can be obtained, leading to a simple method for model selection that controls the overall error rate for incorrect edge inclusion. The simultaneous p-values corresponding to the partial correlations are partitioned into three disjoint sets, a significant set S, an indeterminate set I and a nonsignificant set N. Our model selection method selects two graphs, a graph ĜSI whose edges correspond to the set S ∪ I, and a more conservative graph ĜS whose edges correspond to S only. Similar considerations apply to covariance graph models, which are defined in terms of marginal independence rather than conditional independence. The method is applied to some well-known examples and to simulated data.

Original languageEnglish
Pages (from-to)591-602
Number of pages12
JournalBiometrika
Volume91
Issue number3
DOIs
StatePublished - 2004
Externally publishedYes

Keywords

  • Concentration graph
  • Covariance graph
  • Covariance selection model
  • Graphical model selection
  • Simultaneous confidence intervals
  • Šidák's inequality

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