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dc.contributor.authorDonnet, Sophie
HAL ID: 14568
ORCID: 0000-0003-4370-7316
dc.contributor.authorRivoirard, Vincent
dc.contributor.authorRousseau, Judith
dc.contributor.authorScricciolo, Catia
dc.subjectposterior concentration rates
dc.subjectcounting processes
dc.subjectAalen model
dc.subjectDirichlet process mixtures
dc.subjectGibbs algorithm
dc.subjectEmpirical Bayes
dc.titlePosterior concentration rates for empirical Bayes procedures, with applications to Dirichlet Process mixtures. Supplementary material
dc.typeDocument de travail / Working paper
dc.contributor.editoruniversityotherDipartimento di Scienze delle Decision Bocconi University;Italie
dc.contributor.editoruniversityotherCentre de Recherche en Économie et Statistique (CREST) INSEE – École Nationale de la Statistique et de l'Administration Économique;France
dc.contributor.editoruniversityotherMathématiques et Informatique Appliquées (MIA) Institut national de la recherche agronomique (INRA) : UMR0518 – AgroParisTech;France
dc.description.abstractenIn this paper we provide general conditions to check on the model and the prior to derive posterior concentration rates for data-dependent priors (or empirical Bayes approaches). We aim at providing conditions that are close to the conditions provided in the seminal paper by \citet{ghosal:vdv:07}. We then apply the general theorem to two different settings: the estimation of a density using Dirichlet process mixtures of Gaussian random variables with base measure depending on some empirical quantities and the estimation of the intensity of a counting process under the Aalen model. A simulation study for inhomogeneous Poisson processes also illustrates our results. In the former case we also derive some results on the estimation of the mixing density and on the deconvolution problem. In the latter, we provide a general theorem on posterior concentration rates for counting processes with Aalen multiplicative intensity with priors not depending on the data. In this supplementary file, we present the Gibbs algorithm used in the numerical example.
dc.relation.ispartofseriestitleUniversité Paris-Dauphine
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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