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

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 163)


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.


Truncated Gaussian vector Rejection sampling Monte Carlo method 



This work has been conducted within the frame of the ReDice Consortium, gathering industrial (CEA, EDF, IFPEN, IRSN, Renault) and academic (Ecole des Mines de Saint-Etienne, INRIA, and the University of Bern) partners around advanced methods for Computer Experiments. The authors wish to thank Olivier Roustant (EMSE), Laurence Grammont (ICJ, Lyon 1) and Yann Richet (IRSN, Paris) for helpful discussions, as well as the anonymous reviewers for constructive comments and the participants of MCQMC2014 conference.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.École Nationale Supérieure des Mines de St-ÉtienneSaint-ÉtienneFrance
  2. 2.Institut Camille Jordan, Université de LyonVilleurbanne CedexFrance
  3. 3.Institut de Radioprotection et de Sûreté Nucléaire (IRSN)Fontenay-aux-RosesFrance

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