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Activity Number: 72
Type: Contributed
Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
Sponsor: Section on Statistical Computing
Abstract - #304671
Title: On Moments and Simulation of Truncated Multivariate T Random Variates
Author(s): Tsung-I Lin*+
Companies: National Chung Hsing University
Address: Dept. of Applied Mathematics, Taichung 402, , Taiwan, Republic of China
Keywords: Auxiliary variable ; Gibbs sampling ; Slice sampling ; Truncated normal distribution ; Truncated t distribution ; Uniform distribution

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.

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