Generalized rejection sampling schemes and applications in signal processing

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dc.contributor.author Martino, Luca
dc.contributor.author Míguez Arenas, Joaquín
dc.date.accessioned 2013-04-05T11:58:08Z
dc.date.available 2013-04-05T11:58:08Z
dc.date.issued 2010-11
dc.identifier.bibliographicCitation Signal Processing, 2010 November, Volume 90, Issue 11, Pages 2981–2995
dc.identifier.issn 0165-1684
dc.identifier.uri http://hdl.handle.net/10016/16625
dc.description The results in this paper(namely those in Section4) have been partially presented at the 34-th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2009)and the 17-th European Signal Processing Conference (EUSIPCO 2009).
dc.description.abstract Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters, have become very popular in signal processing over the last years. However, in many problems of practical interest these techniques demand procedures for sampling from probability distributions with non-standard forms, hence we are often brought back to the consideration of fundamental simulation algorithms, such as rejection sampling (RS). Unfortunately, the use of RS techniques demands the calculation of tight upper bounds for the ratio of the target probability density function (pdf) over the proposal density from which candidate samples are drawn. Except for the class of log-concave target pdf's, for which an efficient algorithm exists, there are no general methods to analytically determine this bound, which has to be derived from scratch for each specific case. In this paper, we introduce new schemes for (a) obtaining upper bounds for likelihood functions and (b) adaptively computing proposal densities that approximate the target pdf closely. The former class of methods provides the tools to easily sample from a posteriori probability distributions (that appear very often in signal processing problems) by drawing candidates from the prior distribution. However, they are even more useful when they are exploited to derive the generalized adaptive RS (GARS) algorithm introduced in the second part of the paper. The proposed GARS method yields a sequence of proposal densities that converge towards the target pdf and enable a very efficient sampling of a broad class of probability distributions, possibly with multiple modes and non-standard forms. We provide some simple numerical examples to illustrate the use of the proposed techniques, including an example of target localization using range measurements, often encountered in sensor network applications.
dc.description.sponsorship This work has been partially supported by the Ministry of Science and Innovation of Spain(project MONIN,ref. TEC-2006-13514-C02-01/TCM,and program Consolider- Ingenio 2010, project CSD2008-00010COMONSENS)and the Autonomous Community of Madrid(project PROMUL- TIDIS-CM, ref.S-0505/TIC/0233).
dc.format.mimetype text/plain
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier
dc.subject.other Rejection sampling
dc.subject.other Adaptive rejectionsampling
dc.subject.other Gibbs sampling
dc.subject.other Particle filtering
dc.subject.other Monte Carlointegration
dc.subject.other Sensor networks
dc.subject.other Target localization
dc.title Generalized rejection sampling schemes and applications in signal processing
dc.type article
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1016/j.sigpro.2010.04.025
dc.subject.eciencia Informática
dc.identifier.doi 10.1016/j.sigpro.2010.04.025
dc.rights.accessRights openAccess
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 2981
dc.identifier.publicationissue 11
dc.identifier.publicationlastpage 2995
dc.identifier.publicationtitle Signal processing
dc.identifier.publicationvolume 90
dc.identifier.uxxi AR/0000007151
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