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Two adaptive rejection sampling schemes for probability density functions log-convex tails

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dc.affiliation.dptoUC3M. Departamento de Teoría de la Señal y Comunicacioneses
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Tratamiento de la Señal y Aprendizaje (GTSA)es
dc.contributor.authorMartino, Luca
dc.contributor.authorMíguez Arenas, Joaquín
dc.date.accessioned2013-06-24T11:08:07Z
dc.date.available2013-06-24T11:08:07Z
dc.date.issued2011-11-21
dc.descriptionDocumento depositado en el repositorio arXiv.org. Versión: arXiv:1111.4942v1 [stat.CO]
dc.description.abstractMonte Carlo methods are often necessary for the implementation of optimal Bayesian estimators. A fundamental technique that can be used to generate samples from virtually any target probability distribution is the so-called rejection sampling method, which generates candidate samples from a proposal distribution and then accepts them or not by testing the ratio of the target and proposal densities. The class of adaptive rejection sampling (ARS) algorithms is particularly interesting because they can achieve high acceptance rates. However, the standard ARS method can only be used with log-concave target densities. For this reason, many generalizations have been proposed. In this work, we investigate two different adaptive schemes that can be used to draw exactly from a large family of univariate probability density functions (pdf's), not necessarily log-concave, possibly multimodal and with tails of arbitrary concavity. These techniques are adaptive in the sense that every time a candidate sample is rejected, the acceptance rate is improved. The two proposed algorithms can work properly when the target pdf is multimodal, with first and second derivatives analytically intractable, and when the tails are log-convex in a infinite domain. Therefore, they can be applied in a number of scenarios in which the other generalizations of the standard ARS fail. Two illustrative numerical examples are shown.
dc.format.extent24
dc.format.mimetypeapplication/pdf
dc.identifier.otherarXiv:1111.4942v1 [stat.CO]
dc.identifier.urihttps://hdl.handle.net/10016/17200
dc.identifier.uxxiAR/0000011721
dc.language.isoeng
dc.publisherUniversidad Carlos III de Madrid. Teoría de la Señal y Comunicaciones
dc.relation.publisherversionhttp://arxiv.org/pdf/1111.4942v1.pdf
dc.rights.accessRightsopen access
dc.subject.ecienciaInformática
dc.subject.ecienciaTelecomunicaciones
dc.subject.otherParticle filtering
dc.subject.otherVolatility models
dc.subject.otherRejection sampling
dc.subject.otherRatio of uniforms method
dc.subject.otherMonte Carlo integration
dc.titleTwo adaptive rejection sampling schemes for probability density functions log-convex tails
dc.typeworking paper*
dc.type.hasVersionSMUR*
dspace.entity.typePublication
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