Journal Article

The normal law under linear restrictions: simulation and estimation via minimax tilting

Botev, Z. I.

2017

Overview

Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing and is typically only feasible by using approximate Markov chain Monte Carlo sampling. We propose a minimax tilting method for exact independently and identically distributed data 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 has a rare vanishing relative error asymptotic property. Numerical experiments suggest that the scheme proposed is accurate in a wide range of set-ups for which competing estimation schemes fail. We give an application to exact independently and identically distributed data simulation from the Bayesian posterior of the probit regression model.

• Publisher: John Wiley & Sons Ltd,Oxford University Press
• Subject: Bayesian analysis / Computer simulation / Data simulation / equations / Estimation / Estimators / Exact simulation / Experiments / Exponential tilting / Linear inequalities / Markov analysis / Markov chain / Mathematical models / Methodology / Minimax technique / Monte Carlo methods / Monte Carlo simulation / Multivariate analysis / Multivariate normal distribution / Normal distribution / Polytope probabilities / Probit posterior simulation / Recurrent / regression analysis / Sampling / Simulation / Statistics / Studies