caa a22 4500 445830891 CHVBK 20180317145314.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10255-011-0110-x doi (NATIONALLICENCE)springer-10.1007/s10255-011-0110-x Efficient algorithms for generating truncated multivariate normal distributions [Elektronische Daten] [Jun-wu Yu, Guo-liang Tian] 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. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 data augmentation nationallicence EM algorithm nationallicence Gibbs sampler nationallicence IBF sampler nationallicence linear inequality constraints nationallicence truncated multivariate normal distribution nationallicence Yu Jun-wu School of Mathematics and Computation Science, Hunan University of Science and Technology, 411201, Xiangtan, China aut Tian Guo-liang Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/4(2011-10-01), 601-612 0168-9673 27:4<601 2011 27 10255 https://doi.org/10.1007/s10255-011-0110-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0110-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yu Jun-wu School of Mathematics and Computation Science, Hunan University of Science and Technology, 411201, Xiangtan, China aut NATIONALLICENCE 700 1- Tian Guo-liang Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/4(2011-10-01), 601-612 0168-9673 27:4<601 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer