Some results on the truncated multivariate t 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.

► We provide explicit matrix expressions for the first two moments of the truncated multivariate t (TMVT) distribution.
► We apply the slice sampling to generate random variates from the TMVT distribution by introducing auxiliary variables.
► We describe an algorithm to draw TMVT samples from a series of full conditionals that are of uniform distributions.
► Practical applications are given to demonstrate the effectiveness and importance of our methodology.