The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting

Abstract

Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing, and is typically only feasible using approximate MCMC sampling. In this article we propose a minimax tilting method for exact iid simulation from the truncated multivariate normal distribution. The new methodology provides both a method for simulation and an efficient estimator to hitherto intractable Gaussian integrals. We prove that the estimator possesses a rare vanishing relative error asymptotic property. Numerical experiments suggest that the proposed scheme is accurate in a wide range of setups for which competing estimation schemes fail. We give an application to exact iid simulation from the Bayesian posterior of the probit regression model.

27 pages; 4 figures, Journal of the Royal Statistical Society: Series B (Statistical Methodology) (2016)

References in corpus (1)

• Three discussions of the paper "sequential quasi-Monte Carlo sampling", by M. Gerber and N. Chopin

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