Covariance decomposition in undirected Gaussian graphical models

Published

Journal Article (Review)

The covariance between two variables in a multivariate Gaussian distribution is decomposed into a sum of path weights for all paths connecting the two variables in an undirected independence graph. These weights are useful in determining which variables are important in mediating correlation between the two path endpoints. The decomposition arises in undirected Gaussian graphical models and does not require or involve any assumptions of causality. This covariance decomposition is derived using basic linear algebra. The decomposition is feasible for very large numbers of variables if the corresponding precision matrix is sparse, a circumstance that arises in examples such as gene expression studies in functional genomics. Additional computational efficiences are possible when the undirected graph is derived from an acyclic directed graph. © 2005 Biometrika Trust.

Full Text

Duke Authors

Cited Authors

  • Jones, B; West, M

Published Date

  • December 1, 2005

Published In

Volume / Issue

  • 92 / 4

Start / End Page

  • 779 - 786

Electronic International Standard Serial Number (EISSN)

  • 1464-3510

International Standard Serial Number (ISSN)

  • 0006-3444

Digital Object Identifier (DOI)

  • 10.1093/biomet/92.4.779

Citation Source

  • Scopus