Covariance decomposition in undirected Gaussian graphical models
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.
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- Statistics & Probability
- 4905 Statistics
- 3802 Econometrics
- 1403 Econometrics
- 0104 Statistics
- 0103 Numerical and Computational Mathematics
Citation
Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 3802 Econometrics
- 1403 Econometrics
- 0104 Statistics
- 0103 Numerical and Computational Mathematics