A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets

Hassan Maatouk 1, 2 Xavier Bay 3, 1
1 DEMO-ENSMSE - Département Décision en Entreprise : Modélisation, Optimisation
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes
Abstract : Statistical researchers have shown increasing interest in generating truncated multivariate normal distributions. In this paper, we only assume that the acceptance region is convex and we focus on rejection sampling. We propose a new algorithm that outperforms crude rejection method for the simulation of truncated multivariate Gaussian random variables. The proposed algorithm is based on a generalization of Von Neumann’s rejection technique which requires the determination of the mode of the truncated multivariate density function. We provide a theoretical upper bound for the ratio of the target probability density function over the proposal probability density function. The simulation results show that the method is especially efficient when the probability of the multivariate normal distribution of being inside the acceptance region is low.
Keywords : Truncated Gaussian vector Rejection sampling Monte Carlo method
Type de document :
Chapitre d'ouvrage
Ronald Cools, Dirk Nuyens. Monte Carlo and Quasi-Monte Carlo Methods, 163, Springer International Publishing, pp 521-530, 2016, Springer Proceedings in Mathematics & Statistics, 〈10.1007/978-3-319-33507-0_27〉
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https://hal-emse.ccsd.cnrs.fr/emse-01339361
Contributeur : Florent Breuil <>
Soumis le : mercredi 29 juin 2016 - 16:16:26
Dernière modification le : jeudi 11 janvier 2018 - 06:22:26

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Hassan Maatouk, Xavier Bay. A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets. Ronald Cools, Dirk Nuyens. Monte Carlo and Quasi-Monte Carlo Methods, 163, Springer International Publishing, pp 521-530, 2016, Springer Proceedings in Mathematics & Statistics, 〈10.1007/978-3-319-33507-0_27〉. 〈emse-01339361〉

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