Sensitivity to hyperprior parameters in Gaussian Bayesian networks

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dc.contributor.authorGómez Villegas, Miguel Ángel
dc.contributor.authorMain Yaque, Paloma
dc.contributor.authorNavarro, H.
dc.contributor.authorSusi García, María Del Rosario
dc.date.accessioned2023-06-19T13:23:14Z
dc.date.available2023-06-19T13:23:14Z
dc.date.issued2014-02
dc.description.abstractBayesian networks (BNs) have become an essential tool for reasoning under uncertainty in complex models. In particular, the subclass of Gaussian Bayesian networks (GBNs) can be used to model continuous variables with Gaussian distributions. Here we focus on the task of learning GBNs from data. Factorization of the multivariate Gaussian joint density according to a directed acyclic graph (DAG) provides an alternative and interchangeable representation of a GBN by using the Gaussian conditional univariate densities of each variable given its parents in the DAG. With this latter conditional specification of a GBN, the learning process involves determination of the mean vector, regression coefficients and conditional variances parameters. Some approaches have been proposed to learn these parameters from a Bayesian perspective using different priors, and therefore some hyperparameter values are tuned. Our goal is to deal with the usual prior distributions given by the normal/inverse gamma form and to evaluate the effect of prior hyperparameter choice on the posterior distribution. As usual in Bayesian robustness, a large class of priors expressed by many hyperparameter values should lead to a small collection of posteriors. From this perspective and using Kullback-Leibler divergence to measure prior and posterior deviations, a local sensitivity measure is proposed to make comparisons. If a robust Bayesian analysis is developed by studying the sensitivity of Bayesian answers to uncertain inputs, this method will also be useful for selecting robust hyperparameter values.en
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Ciencia, Innovación y Universidades (España)
dc.description.sponsorshipMetodos Bayesianos, BSCH-UCM, Spain
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/24698
dc.identifier.citationGómez Villegas, M. A., Main Yaque, P., Navarro, H. & Susi García, M. R. «Sensitivity to Hyperprior Parameters in Gaussian Bayesian Networks». Journal of Multivariate Analysis, vol. 124, febrero de 2014, pp. 214-25. DOI.org (Crossref), https://doi.org/10.1016/j.jmva.2013.10.022.
dc.identifier.doi10.1016/j.jmva.2013.10.022
dc.identifier.issn0047-259X
dc.identifier.officialurlhttps//doi.org/10.1016/j.jmva.2013.10.022
dc.identifier.relatedurlhttp://www.sciencedirect.com/science/article/pii/S0047259X13002340
dc.identifier.urihttps://hdl.handle.net/20.500.14352/33474
dc.journal.titleJournal of multivariate analysis
dc.language.isoeng
dc.page.final225
dc.page.initial214
dc.publisherElsevier
dc.relation.projectIDMTM 2008 . 03282
dc.relation.projectIDGR58/08-A
dc.relation.projectID910395
dc.rights.accessRightsopen access
dc.subject.cdu519.2
dc.subject.keywordGaussian Bayesian network
dc.subject.keywordKullback-Leibler divergence
dc.subject.keywordBayesian linear regression
dc.subject.ucmEstadística matemática (Matemáticas)
dc.subject.unesco1209 Estadística
dc.titleSensitivity to hyperprior parameters in Gaussian Bayesian networksen
dc.typejournal article
dc.volume.number124
dspace.entity.typePublication
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