標題: ON SPHERICAL MONTE CARLO SIMULATIONS FOR MULTIVARIATE NORMAL PROBABILITIES
作者: Teng, Huei-Wen
Kang, Ming-Hsuan
Fuh, Cheng-Der
交大名義發表
National Chiao Tung University
關鍵字: Spherical;simulation;variance reduction;sphere packings;kissing number;lattice
公開日期: 1-九月-2015
摘要: The calculation of multivariate normal probabilities is of great importance in many statistical and economic applications. In this paper we propose a spherical Monte Carlo method with both theoretical analysis and numerical simulation. We start by writing the multivariate normal probability via an inner radial integral and an outer spherical integral using the spherical transformation. For the outer spherical integral, we apply an integration rule by randomly rotating a predetermined set of well-located points. To find the desired set, we derive an upper bound for the variance of the Monte Carlo estimator and propose a set which is related to the kissing number problem in sphere packings. For the inner radial integral, we employ the idea of antithetic variates and identify certain conditions so that variance reduction is guaranteed. Extensive Monte Carlo simulations on some probabilities confirm these claims.
URI: http://hdl.handle.net/11536/128293
ISSN: 0001-8678
期刊: ADVANCES IN APPLIED PROBABILITY
Volume: 47
起始頁: 817
結束頁: 836
顯示於類別:期刊論文