期刊
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
卷 142, 期 1, 页码 25-40出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.jspi.2011.06.006
关键词
Auxiliary variable; Gibbs sampling; Slice sampling; Truncated normal distribution; Truncated t distribution; Uniform distribution
资金
- National Science Council of Taiwan [NSC99-2118-M-005-001-MY2, NSC99-2118-M-035-004]
The use of truncated distributions arises often in a wide variety of scientific problems. In the literature, there are a lot of sampling schemes and proposals developed for various specific truncated distributions. So far, however, the study of the truncated multivariate t (TMVT) distribution is rarely discussed. In this paper, we first present general formulae for computing the first two moments of the TMVT distribution under the double truncation. We formulate the results as analytic matrix expressions, which can be directly computed in existing software. Results for the left and right truncation can be viewed as special cases. We then apply the slice sampling algorithm to generate random variates from the TMVT distribution by introducing auxiliary variables. This strategic approach can result in a series of full conditional densities that are of uniform distributions. Finally, several examples and practical applications are given to illustrate the effectiveness and importance of the proposed results. (C) 2011 Elsevier B.V. All rights reserved.
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