Automatic tempered posterior distributions for bayesian inversion problems

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Show simple item record Martino, Luca Llorente Fernández, Fernando Curbelo Benitez, Ernesto Angel López Santiago, Javier Míguez Arenas, Joaquín 2021-10-25T11:29:46Z 2021-10-25T11:29:46Z 2021-04-01
dc.identifier.bibliographicCitation Martino, L., Llorente, F., Curbelo, E., López-Santiago, J. & Míguez, J. (2021). Automatic Tempered Posterior Distributions for Bayesian Inversion Problems. Mathematics, 9(7), 784.
dc.identifier.issn 2227-7390
dc.description.abstract We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise are carried out using distinct (but interacting) methods. More specifically, we consider a Bayesian analysis for the variables of interest (i.e., the parameters of the model to invert), whereas we employ a maximum likelihood approach for the estimation of the noise power. The whole technique is implemented by means of an iterative procedure with alternating sampling and optimization steps. Moreover, the noise power is also used as a tempered parameter for the posterior distribution of the the variables of interest. Therefore, a sequence of tempered posterior densities is generated, where the tempered parameter is automatically selected according to the current estimate of the noise power. A complete Bayesian study over the model parameters and the scale parameter can also be performed. Numerical experiments show the benefits of the proposed approach.
dc.description.sponsorship This work was partially supported by the Office of Naval Research (award no. N00014-19-1-2226), the Spanish Ministry of Science and Innovation (RTI2018-099655-B- I00 CLARA and PID2019-105032GB-I00 SPGRAPH), the Foundation by the Community of Madrid in the framework of the Multiannual Agreement with the Rey Juan Carlos University in line of action 1, Encouragement of Young Ph.D. students investigation Project under Grant F661, and the regional Government of Madrid (Comunidad de Madrid, reference Y2018/TCS-4705 PRACTICO).
dc.format.extent 17
dc.language.iso eng
dc.publisher MDPI
dc.rights © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
dc.rights Atribución 3.0 España
dc.subject.other Bayesian inference
dc.subject.other Importance sampling
dc.subject.other MCMC
dc.subject.other Inversion problems
dc.title Automatic tempered posterior distributions for bayesian inversion problems
dc.type article
dc.subject.eciencia Estadística
dc.subject.eciencia Telecomunicaciones
dc.rights.accessRights openAccess
dc.relation.projectID Comunidad de Madrid. Y2018/TCS-4705
dc.relation.projectID Gobierno de España. RTI2018-099655-B-I00
dc.relation.projectID Gobierno de España. PID2019-105032GB-I00
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 784
dc.identifier.publicationissue 7
dc.identifier.publicationtitle Mathematics
dc.identifier.publicationvolume 9
dc.identifier.uxxi AR/0000028411
dc.contributor.funder Comunidad de Madrid
dc.contributor.funder Ministerio de Ciencia e Innovación (España)
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