Publication:
Adaptive posterior distributions for covariance matrix learning in Bayesian inversion problems for multioutput signals

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dc.affiliation.dptoUC3M. Departamento de Estadísticaes
dc.contributor.authorCurbelo Benitez, Ernesto Angel
dc.contributor.authorMartino, Luca
dc.contributor.authorLlorente Fernandez, Fernando
dc.contributor.authorDelgado Gómez, David
dc.contributor.editorUniversidad Carlos III de Madrid. Departamento de Estadísticaes
dc.date.accessioned2023-05-30T14:15:02Z
dc.date.available2023-05-30T14:15:02Z
dc.date.issued2023-05-30
dc.description.abstractIn this work, we propose an adaptive importance sampling (AIS) scheme for multivariate Bayesian inversion problems, which is based in two main ideas: the inference procedure is divided in two parts and the variables of interest are split in two blocks. We assume that the observations are generated from a complex multivariate non-linear function perturbed by correlated Gaussian noise. We estimate both the unknown parameters of the multivariate non-linear model and the covariance matrix of the noise. In the first part of the proposed inference scheme, a novel AIS technique called adaptive target AIS (ATAIS) is designed, which alternates iteratively between an IS technique over the parameters of the non-linear model and a frequentist approach for the covariance matrix of the noise. In the second part of the proposed inference scheme, a prior density over the covariance matrix is considered and the cloud of samples obtained by ATAIS are recycled and re-weighted for obtaining a complete Bayesian study over the model parameters and covariance matrix. Two numerical examples are presented that show the benefits of the proposed approach.en
dc.identifier.issn2387-0303
dc.identifier.urihttps://hdl.handle.net/10016/37391
dc.identifier.uxxiDT/0000002075es
dc.language.isoenges
dc.relation.ispartofseriesWorking paper Statistics and Econometricsen
dc.relation.ispartofseries23-05
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaEstadísticaes
dc.subject.otherBayesian Inversionen
dc.subject.otherImportance Samplingen
dc.subject.otherCovariance Matrixen
dc.subject.otherTemperingen
dc.subject.otherSequence Of Posteriorsen
dc.titleAdaptive posterior distributions for covariance matrix learning in Bayesian inversion problems for multioutput signalsen
dc.typeworking paper*
dspace.entity.typePublication
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