Simulation from Wishart distributions with eigenvalue constraints

This article provides an efficient algorithm for generating a random matrix according to a Wishart distribution, but with eigenvalues constrained to b e less than a given vector of positive values. The procedure of Odell and F eiveson provides a guide, but the modifications here ensure that the diagon al elements of a candidate matrix are less than the corresponding elements of the constraint vector, thus greatly improving the chances that the matri x will be acceptable. The Normal hierarchical model with vector outcomes an d the multivariate random effects model provide motivating applications.