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Efficient Algorithms for Generating Truncated Multivariate Normal Distributions

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Yu Junwu 1 *   Tian Guoliang 2  
文摘 Sampling from a truncated multivariate normal distribution (TMVND) constitutes the core computational module in fitting many statistical and econometric models. We propose two efficient methods, an iterative data augmentation (DA) algorithm and a non-iterative inverse Bayes formulae (IBF) sampler, to simulate TMVND and generalize them to multivariate normal distributions with linear inequality constraints. By creating a Bayesian incomplete-data structure, the posterior step of the DA algorithm directly generates random vector draws as opposed to single element draws, resulting obvious computational advantage and easy coding with common statistical software packages such as S-PLUS, MATLAB and GAUSS. Furthermore, the DA provides a ready structure for implementing a fast EM algorithm to identify the mode of TMVND, which has many potential applications in statistical inference of constrained parameter problems. In addition, utilizing this mode as an intermediate result, the IBF sampling provides a novel alternative to Gibbs sampling and eliminates problems with convergence and possible slow convergence due to the high correlation between components of a TMVND. The DA algorithm is applied to a linear regression model with constrained parameters and is illustrated with a published data set. Numerical comparisons show that the proposed DA algorithm and IBF sampler are more efficient than the Gibbs sampler and the accept-reject algorithm.
来源 Acta Mathematicae Applicatae Sinica-English Series ,2011,27(4):601-612 【核心库】
DOI 10.1007/s10255-011-0110-x
关键词 data augmentation ; EM algorithm ; Gibbs sampler ; IBF sampler ; linear inequality constraints ; truncated multivariate normal distribution
地址

1. School of Mathematics and Computation Science, Hunan University of Science and Technology, Xiangtan, 411201  

2. Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong

语种 英文
文献类型 研究性论文
ISSN 0168-9673
学科 数学
基金 国家社会科学基金 ;  湖南省教育厅项目 ;  HKU Seed Funding Program for Basic Research ;  Hong Kong Research Grant Council-General Research Fund
文献收藏号 CSCD:4323981

参考文献 共 38 共2页

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引证文献 1 篇

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