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

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Show simple item record Martino, Luca Míguez Arenas, Joaquín 2013-06-24T11:08:07Z 2013-06-24T11:08:07Z 2011-11-21
dc.identifier.other arXiv:1111.4942v1 [stat.CO]
dc.description Documento depositado en el repositorio Versión: arXiv:1111.4942v1 [stat.CO]
dc.description.abstract Monte 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.extent 24
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Universidad Carlos III de Madrid. Teoría de la Señal y Comunicaciones
dc.subject.other Particle filtering
dc.subject.other Volatility models
dc.subject.other Rejection sampling
dc.subject.other Ratio of uniforms method
dc.subject.other Monte Carlo integration
dc.title Two adaptive rejection sampling schemes for probability density functions log-convex tails
dc.type workingPaper
dc.subject.eciencia Informática
dc.subject.eciencia Telecomunicaciones
dc.rights.accessRights openAccess
dc.type.version submitedVersion
dc.identifier.uxxi AR/0000011721
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