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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2016
- DOI:
- 10.48550/arXiv.1603.04166
- arXiv:
- arXiv:1603.04166
- Bibcode:
- 2016arXiv160304166B
- Keywords:
-
- Statistics - Computation;
- 65C05;
- 68W20
- E-Print:
- 27 pages