Computing and approximating multivariate chi-square probabilities

Abstract

We consider computational methods for evaluating and approximating multivariate chi-square probabilities in cases where the pertaining correlation matrix or blocks thereof have a low-factorial representation. To this end, techniques from matrix factorization and probability theory are applied. We outline a variety of statistical applications of multivariate chi-square distributions and provide a system of MATLAB programs implementing the proposed algorithms. Computer simulations demonstrate the accuracy and the computational efficiency of our methods in comparison with Monte Carlo approximations, and a real data example from statistical genetics illustrates their usage in practice.