Gaussian Covariance Faithful Markov Trees
Joint Authors
Rajaratnam, Bala
Malouche, Dhafer
Source
Journal of Probability and Statistics
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-12-11
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Graphical models are useful for characterizing conditional and marginal independence structures in high-dimensional distributions.
An important class of graphical models is covariance graph models, where the nodes of a graph represent different components of a random vector, and the absence of an edge between any pair of variables implies marginal independence.
Covariance graph models also represent more complex conditional independence relationships between subsets of variables.
When the covariance graph captures or reflects all the conditional independence statements present in the probability distribution, the latter is said to be faithful to its covariance graph—though in general this is not guaranteed.
Faithfulness however is crucial, for instance, in model selection procedures that proceed by testing conditional independences.
Hence, an analysis of the faithfulness assumption is important in understanding the ability of the graph, a discrete object, to fully capture the salient features of the probability distribution it aims to describe.
In this paper, we demonstrate that multivariate Gaussian distributions that have trees as covariance graphs are necessarily faithful.
American Psychological Association (APA)
Malouche, Dhafer& Rajaratnam, Bala. 2011. Gaussian Covariance Faithful Markov Trees. Journal of Probability and Statistics،Vol. 2011, no. 2011, pp.1-10.
https://search.emarefa.net/detail/BIM-450010
Modern Language Association (MLA)
Malouche, Dhafer& Rajaratnam, Bala. Gaussian Covariance Faithful Markov Trees. Journal of Probability and Statistics No. 2011 (2011), pp.1-10.
https://search.emarefa.net/detail/BIM-450010
American Medical Association (AMA)
Malouche, Dhafer& Rajaratnam, Bala. Gaussian Covariance Faithful Markov Trees. Journal of Probability and Statistics. 2011. Vol. 2011, no. 2011, pp.1-10.
https://search.emarefa.net/detail/BIM-450010
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-450010