A new rejection sampling method for truncated multivariate Gaussian random variables restricted to convex sets
| Autor: | Hassan Maatouk, Xavier Bay |
|---|---|
| Přispěvatelé: | Ecole Nationale Supérieure des Mines de St Etienne, Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Institut Henri Fayol (FAYOL-ENSMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, Ronald Cools and Dirk Nuyens, Département Décision en Entreprise : Modélisation, Optimisation (DEMO-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Henri Fayol, Institut Mines-Télécom [Paris] (IMT), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne (UCA)-Centre National de la Recherche Scientifique (CNRS), Ronald Cools, Dirk Nuyens, Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Truncated Gaussian vector
Truncated normal distribution Rejection sampling MathematicsofComputing_NUMERICALANALYSIS Slice sampling Multivariate normal distribution 010502 geochemistry & geophysics 01 natural sciences [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation Monte Carlo method [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010104 statistics & probability symbols.namesake Joint probability distribution Statistics ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION symbols Applied mathematics Multivariate t-distribution 0101 mathematics Gaussian process Random variable 0105 earth and related environmental sciences Mathematics |
| Zdroj: | Monte Carlo and Quasi-Monte Carlo Methods Ronald Cools and 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⟩ 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⟩ Springer Proceedings in Mathematics & Statistics ISBN: 9783319335056 MCQMC |
| DOI: | 10.1007/978-3-319-33507-0_27⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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