Accession Number : ADP007100

Title :   Graphical Models and their Representation,

Corporate Author : PRINCETON UNIV NJ

Personal Author(s) : Goodall, Colin ; Thoma, H. M.

Report Date : 1992

Pagination or Media Count : 8

Abstract : In a multivariate Gaussian model, the presence of a zero in the inverse variance matrix, or in the partial correlation matrix, implies that the two variables are independent given the rest. Thus the dependence between variables can be fully represented by a graph, in which the absence of an edge implies conditional independence. This leads to the term graphical Gaussian model, and further to theorems concerning the equivalence of the local, global and pairwise Markov properties of the graphical model. For discrete distributions (or other multivariate continuous distributions), this graphical representation is ambiguous, as the interactions may involve more than two variables at a time. By convention, the presence of a clique of kappa variables in a graph representing a cross-classified multinomial distribution implies that the joint distribution includes a term in all kappa variables. The distribution does not in general factorize into (kappa/2) pairwise components. However, a hypergraph gives a natural, unambiguous, representation.

Descriptors :   *COMPUTER GRAPHICS, *MULTIVARIATE ANALYSIS, CORRELATION, DISTRIBUTION, EDGES, GLOBAL, GRAPHS, INTERACTIONS, MODELS, REST, THEOREMS, TIME, VARIABLES.

Subject Categories : Statistics and Probability
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE