Efficient algorithms for generating truncated multivariate normal distributions |
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Authors: | Jun-wu Yu Guo-liang Tian |
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Institution: | Jun-wu YU 1,Guo-liang TIAN 2 1 School of Mathematics and Computation Science,Hunan University of Science and Technology,Xiangtan 411201,China 2 Department of Statistics and Actuarial Science,The University of Hong Kong,Pokfulam Road,Hong Kong,China |
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Abstract: | 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. |
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Keywords: | data augmentation EM algorithm Gibbs sampler IBF sampler linear inequality constraints truncated multivariate normal distribution |
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