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- ItemComputing and approximating multivariate chi-square probabilities(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Stange, Jens; Loginova, Nina; Dickhaus, ThorstenWe 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.