Graphical Models and their Representation,
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1992
- Accession Number
- ADP007100
Entities
People
- Colin Goodall
- H. M. Thoma
Organizations
- Princeton University