Fast and Exact Simulation of Multivariate Normal and Wishart Random Variables with Box Constraints

Models which include domain constraints occur in myriad contexts such as econometrics, genomics, and environmetrics, though simulating from constrained distributions can be computationally expensive. In particular, repeated sampling from constrained distributions is a common task in Bayesian inferential methods, where coping with these constraints can cause troublesome computational burden. Here, we introduce computationally efficient methods to make exact and independent draws from both the multivariate normal and Wishart distributions with box constraints. In both cases, these variables are sampled using a direct algorithm. By substantially reducing computing time, these new algorithms improve the feasibility of Monte Carlo-based inference for box-constrained, multivariate normal and Wishart distributions.