Efficient probability estimation and simulation of the truncated multivariate student-t distribution

We propose an exponential tilting method for the accurate estimation of the probability that a random vector with multivariate student-t distribution falls in a convex polytope. The method can also be used to simulate exactly from the corresponding truncated multivariate student-t distribution, thus providing an alternative to approximate Markov Chain Monte Carlo simulation. Numerical experiments show that the suggested method is significantly more accurate and reliable than its competitors.