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Article: Efficient algorithms for generating truncated multivariate normal distributions

TitleEfficient algorithms for generating truncated multivariate normal distributions
Authors
KeywordsData Augmentation
Em Algorithm
Gibbs Sampler
Ibf Sampler
Linear Inequality Constraints
Truncated Multivariate Normal Distribution
Issue Date2011
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/10255/
Citation
Acta Mathematicae Applicatae Sinica, 2011, v. 27 n. 4, p. 601-612 How to Cite?
AbstractSampling from a truncated multivariate normal distribution (TMVND) constitutes the core computational module in fitting many statistical and econometric models. We propose two efficient methods, an iterative data augmentation (DA) algorithm and a non-iterative inverse Bayes formulae (IBF) sampler, to simulate TMVND and generalize them to multivariate normal distributions with linear inequality constraints. By creating a Bayesian incomplete-data structure, the posterior step of the DA algorithm directly generates random vector draws as opposed to single element draws, resulting obvious computational advantage and easy coding with common statistical software packages such as S-PLUS, MATLAB and GAUSS. Furthermore, the DA provides a ready structure for implementing a fast EM algorithm to identify the mode of TMVND, which has many potential applications in statistical inference of constrained parameter problems. In addition, utilizing this mode as an intermediate result, the IBF sampling provides a novel alternative to Gibbs sampling and eliminates problems with convergence and possible slow convergence due to the high correlation between components of a TMVND. The DA algorithm is applied to a linear regression model with constrained parameters and is illustrated with a published data set. Numerical comparisons show that the proposed DA algorithm and IBF sampler are more efficient than the Gibbs sampler and the accept-reject algorithm. © 2011 Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.
Persistent Identifierhttp://hdl.handle.net/10722/172483
ISSN
2015 Impact Factor: 0.25
2015 SCImago Journal Rankings: 0.220
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorYu, JWen_US
dc.contributor.authorTian, GLen_US
dc.date.accessioned2012-10-30T06:22:45Z-
dc.date.available2012-10-30T06:22:45Z-
dc.date.issued2011en_US
dc.identifier.citationActa Mathematicae Applicatae Sinica, 2011, v. 27 n. 4, p. 601-612en_US
dc.identifier.issn0168-9673en_US
dc.identifier.urihttp://hdl.handle.net/10722/172483-
dc.description.abstractSampling from a truncated multivariate normal distribution (TMVND) constitutes the core computational module in fitting many statistical and econometric models. We propose two efficient methods, an iterative data augmentation (DA) algorithm and a non-iterative inverse Bayes formulae (IBF) sampler, to simulate TMVND and generalize them to multivariate normal distributions with linear inequality constraints. By creating a Bayesian incomplete-data structure, the posterior step of the DA algorithm directly generates random vector draws as opposed to single element draws, resulting obvious computational advantage and easy coding with common statistical software packages such as S-PLUS, MATLAB and GAUSS. Furthermore, the DA provides a ready structure for implementing a fast EM algorithm to identify the mode of TMVND, which has many potential applications in statistical inference of constrained parameter problems. In addition, utilizing this mode as an intermediate result, the IBF sampling provides a novel alternative to Gibbs sampling and eliminates problems with convergence and possible slow convergence due to the high correlation between components of a TMVND. The DA algorithm is applied to a linear regression model with constrained parameters and is illustrated with a published data set. Numerical comparisons show that the proposed DA algorithm and IBF sampler are more efficient than the Gibbs sampler and the accept-reject algorithm. © 2011 Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.en_US
dc.languageengen_US
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/10255/en_US
dc.relation.ispartofActa Mathematicae Applicatae Sinicaen_US
dc.subjectData Augmentationen_US
dc.subjectEm Algorithmen_US
dc.subjectGibbs Sampleren_US
dc.subjectIbf Sampleren_US
dc.subjectLinear Inequality Constraintsen_US
dc.subjectTruncated Multivariate Normal Distributionen_US
dc.titleEfficient algorithms for generating truncated multivariate normal distributionsen_US
dc.typeArticleen_US
dc.identifier.emailTian, GL: gltian@hku.hken_US
dc.identifier.authorityTian, GL=rp00789en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1007/s10255-011-0110-xen_US
dc.identifier.scopuseid_2-s2.0-80052497028en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-80052497028&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume27en_US
dc.identifier.issue4en_US
dc.identifier.spage601en_US
dc.identifier.epage612en_US
dc.identifier.isiWOS:000294786700005-
dc.publisher.placeGermanyen_US
dc.identifier.scopusauthoridYu, JW=16204381100en_US
dc.identifier.scopusauthoridTian, GL=25621549400en_US

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