Marginal Densities of the Wishart Distribution

2010 Mathematics Subject Classification: 62H10.

We consider marginal densities obtained by elimination of non-diagonal elements of a positive definite random matrix with an arbitrary distribution. For a p × p random matrix W such a marginal density is presented by a graph with p vertices. For every non-diagonal element of W, included in the density we draw in the graph an undirected edge between the corresponding vertices. By giving an equivalent definition of decomposable graphs we show that the bounds of the integration with respect to every excluded element of W can be exactly obtained if and only if the corresponding graph is decomposable. The author gives in an explicit form some of the marginal densities of an arbitrary Wishart distribution.