Numerical Computation of Multivariate Normal and Multivariate-t Probabilities over Convex Regions

Numerical Computation of Multivariate Normal Probabilities

The numerical computation of a multivariate normal probability is often a diicult problem. This article describes a transformation that simpliies the problem and places it into a form that allows eecient calculation using standard numerical multiple integration algorithms. Test results are presented that compare implementations of two algorithms that use the transformation, with currently avail...

Parallel Computation of Multivariate Normal Probabilities

We present methods for the computation of multivari-ate normal probabilities on parallel/ distributed systems. After a transformation of the initial integral, an approximation can be obtained using Monte-Carlo or quasi-random methods. We propose a meta-algorithm for asynchronous sampling methods and derive eecient parallel algorithms for the computation of MVN distribution functions, including ...

Comparison of Methods for the Computation Of Multivariate t-Probabilities

Methods for the Computation of Multivariate t - Probabilities ∗

This paper compares methods for the numerical computation of multivariate t-probabilities for hyperrectangular integration regions. Methods based on acceptance-rejection, spherical-radial transformations and separation-of-variables transformations are considered. Tests using randomly chosen problems show that the most efficient numerical methods use a transformation developed by Genz (1992) for...

Numerical Computation of Multivariate T- Probabilities with Application to Power Calculation of Multiple Contrasts

A new method to calculate the multivariate t-distribution is introduced. We provide a series of substitutions, which transform the starting q-variate integral into one over the q 1 1 6 dimensional hypercube. In this situation standard numerical integration methods can be applied. Three algorithms are discussed in detail. As an application we derive an expression to calculate the power of multip...