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

被引:138
作者
Botev, Z. I. [1 ]
机构
[1] Univ New South Wales, Sydney, NSW, Australia
基金
澳大利亚研究理事会;
关键词
Exact simulation; Exponential tilting; Linear inequalities; Multivariate normal distribution; Polytope probabilities; Probit posterior simulation; MULTIVARIATE NORMAL PROBABILITIES; ORTHANT PROBABILITIES; GAUSSIAN DISTRIBUTIONS; T-PROBABILITIES; MONTE-CARLO; COMPUTATION; SYSTEMS;
D O I
10.1111/rssb.12162
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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.
引用
收藏
页码:125 / 148
页数:24
相关论文
共 42 条
[1]   BAYESIAN-ANALYSIS OF BINARY AND POLYCHOTOMOUS RESPONSE DATA [J].
ALBERT, JH ;
CHIB, S .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1993, 88 (422) :669-679
[2]  
[Anonymous], 2007, Bayesian econometric methods
[3]  
[Anonymous], NUMER METHR NONLINEA
[4]  
[Anonymous], 1991, COMPUTING SCI STAT
[5]  
[Anonymous], 2011, WILEY SERIES PROBABI
[6]   Simultaneous confidence bands in curve prediction applied to load curves [J].
Azais, J. M. ;
Bercu, S. ;
Fort, J. C. ;
Lagnoux, A. ;
Le, P. .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS, 2010, 59 :889-904
[7]   Excursion and contour uncertainty regions for latent Gaussian models [J].
Bolin, David ;
Lindgren, Finn .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2015, 77 (01) :85-106
[8]  
Botev Z. I., 2015, P WINT SIM IN PRESS
[9]   Markov chain importance sampling with applications to rare event probability estimation [J].
Botev, Zdravko I. ;
L'Ecuyer, Pierre ;
Tuffin, Bruno .
STATISTICS AND COMPUTING, 2013, 23 (02) :271-285
[10]   An accept-reject algorithm for the positive multivariate normal distribution [J].
Botts, Carsten .
COMPUTATIONAL STATISTICS, 2013, 28 (04) :1749-1773