TY - JOUR
A2 - Gao, Junbin B.
AU - Malouche, Dhafer
AU - Rajaratnam, Bala
PY - 2011
DA - 2011/12/11
TI - Gaussian Covariance Faithful Markov Trees
SP - 152942
VL - 2011
AB - 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.
SN - 1687-952X
UR - https://doi.org/10.1155/2011/152942
DO - 10.1155/2011/152942
JF - Journal of Probability and Statistics
PB - Hindawi Publishing Corporation
KW -
ER -