Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results
多元正态矩形概率及其导数的模拟：理论与计算结果
An extensive literature in econometrics and in numerical analysis has considered the problem of evaluating the multiple integral P(B; μ, Ω) = ∝ab n(v − μ, Ω)dv ≡ Ev1(V ϵ B), where V is a m-dimensional normal vector with mean μ, covariance matrix Ω, and density n(v − μ, Ω), and 1(V ϵ B) is an indicator for the event B = (V¦a < V < b). A leading case of such an integral is the negative orthant probability, where B = (V ¦V < 0). The problem is computationally difficult except…