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

TL;DR

This paper introduces a minimax tilting method for exact iid simulation from high-dimensional truncated multivariate normal distributions, enabling efficient estimation of Gaussian integrals with vanishing relative error.

Contribution

It presents a novel minimax tilting approach for exact iid simulation and efficient estimation of Gaussian integrals, outperforming existing methods in accuracy and applicability.

Findings

The estimator has a vanishing relative error asymptotic property.

Numerical experiments show high accuracy across various setups.

Application to Bayesian probit regression demonstrates practical utility.

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.