多维正态分布的数值计算

The Numerical Computation of Multivariate Normal Probabilities

为了克服多维正态分布积分计算量过大的问题,引入多维正态分布积分的一种降维的变换形式,对变换后的积分运用蒙特卡洛以及拟蒙特卡洛算法进行计算求值.在此基础上,提出一种改进的方法,并做了相应的数值试验.

The computation of a multivariate normal probability is very difficult. This article describes a series of substitutions which reduce dimensions by transforming the m - variate integral into one over the （ m - 1 ） - dimensional hypercube. Monte Carlo and quasi - Monte Carlo methods are introduced to solve the problem. Then, an improved algorithm is presented and corresponding numerical experiments are conducted.