A new rejection sampling method for truncated multivariate Gaussian random variables
Abstract
Statistical researchers have shown increased interest in generating of truncated
multivariate normal distributions. In this paper, we assume that the acceptance
region is convex and our focus is on the rejection sampling. We propose a new
algorithm that outperforms crude rejection method for the simulation of truncated
multivariate normal distribution. Our algorithm is based on a generalization of
Von Neumann’s rejection technique which requires the determination of the mode
of the truncated multivariate density function. We provide a theoretical upper
bound for the ratio of the target probability density function that the proposed
density function is defined from the mode. This algorithm is used in the case where
the maximum likelihood lies outside the acceptance region and the dimension of
the multivariate density is high. The simulation results show that using rejection
sampling from the mode is more efficient than the usual rejection sampling. In
order to support the theoretical aspect of our work, we have used an illustrative
example.