Efficient Simulation from the Multivariate Normal and Student-t Distributions Subject to Linear Constraints and the Evaluation of Constraint Probabilities

Abstract

The construction and implementation of a Gibbs sampler for efficient simulation from the truncated multivariate normal and Student-t distributions is described. It is shown how the accuracy and convergence of integrals based on the Gibbs sample may be constructed, and how an estimate of the probability of the constraint set under the unrestricted distribution may be produced. Keywords: Bayesian inference; Gibbs sampler; Monte Carlo; multiple integration; truncated normal This paper was prepared for a presentation at the meeting Computing Science and Statistics: the Twenty-Third Symposium on the Interface, Seattle, April 22-24, 1991. Research assistance from Zhenyu Wang and financial support from National Science Foundation Grant SES-8908365 are gratefully acknowledged. The software for the examples may be requested by electronic mail, and will be returned by that medium. 2 1. Introduction The generation of random samples from a truncated multivariate normal distribution, that is, a ...