Directional simulation in Gaussian processes

Abstract Aiming at reducing the sampling variance of the estimated probability on a given set, a generalization is given of the method of uniform mean centred directional sampling in the standardized n- dimensional Gaussian space. Two modifications of different nature are involved. The one consists in shifting the origin to a point different from the mean. The resulting off-mean centred directional simulation method is operational due to the existence of a closed form generalized chi-square distribution function for the square of the distance from the origin to the Gaussain random point. Suitable choices of the origin give considerably reduced sampling variances in most cases. Secondly there is a possibility of variance reduction by defining the sampling distribution in such a way that the exact probability on a given half-space is obtained by a single simulation. Comparative effectivity studies for different examples are made. Finally the method is also set up for computing mean outcrossing rates for Gaussian vector processes.