A q-exponential statistical Banach manifold

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dc.citation.epage466spa
dc.citation.issue2spa
dc.citation.journalTitleJournal of Mathematical Analysis and Applicationsspa
dc.citation.spage476spa
dc.citation.volume398spa
dc.contributor.authorQuiceno Echavarría, Héctor Román
dc.contributor.authorLoaiza Ossa, Gabriel Ignacio
dc.contributor.departmentdepartment:Universidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y Aplicaciones
dc.contributor.eafitauthorHéctor R. Quiceno (hquiceno@eafit.edu.co)spa
dc.contributor.eafitauthorGabriel Loaiza (gloaiza@eafit.edu.co)spa
dc.contributor.researchgroupAnálisis Funcional y Aplicacionesspa
dc.date.accessioned2015-04-24T16:18:49Z
dc.date.available2015-04-24T16:18:49Z
dc.date.issued2013-02
dc.description.abstractLetµbe a given probability measure andMµ the set ofµ-equivalent strictly positive probability densities -- In this paper we construct a Banach manifold on Mµ, modeled on the space L∞(p · µ) where p is a reference density, for the non-parametric q-exponential statistical models (Tsallis’s deformed exponential), where 0 < q < 1 is any real number -- This family is characterized by the fact that when q → 1, then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space -- The coordinate mappings of the manifold are given in terms of Csiszár’s Φ-divergences; the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score functionspa
dc.description.abstractLetµbe a given probability measure andMµ the set ofµ-equivalent strictly positive probability densities -- In this paper we construct a Banach manifold on Mµ, modeled on the space L∞(p · µ) where p is a reference density, for the non-parametric q-exponential statistical models (Tsallis’s deformed exponential), where 0 < q < 1 is any real number -- This family is characterized by the fact that when q → 1, then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space -- The coordinate mappings of the manifold are given in terms of Csiszár’s Φ-divergences; the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score functioneng
dc.identifier.citationG. Loaiza, H.R. Quiceno, A -exponential statistical Banach manifold, Journal of Mathematical Analysis and Applications, Volume 398, Issue 2, 15 February 2013, Pages 466-476, ISSN 0022-247X, http://dx.doi.org/10.1016/j.jmaa.2012.08.046. (http://www.sciencedirect.com/science/article/pii/S0022247X12006981)spa
dc.identifier.doi10.1016/j.jmaa.2012.08.046
dc.identifier.issn0022-247Xspa
dc.identifier.urihttp://hdl.handle.net/10784/5245
dc.language.isoengeng
dc.publisherELSEVIERspa
dc.relation.ispartofJournal of Mathematical Analysis and Applications Volume 398, Issue 2, 15 February 2013, Pages 466–476spa
dc.relation.urihttp://dx.doi.org/10.1016/j.jmaa.2012.08.046
dc.rightsCopyright © 2012 Elsevier Ltd. All rights reserved.spa
dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccessspa
dc.rights.localAcceso restringidospa
dc.subject.keywordInformation theoryeng
dc.subject.keywordEntropy (information theory)eng
dc.subject.keywordBanach spaceseng
dc.subject.keywordQuantum physicaleng
dc.subject.keywordMathematical analysiseng
dc.subject.keywordGeometry, differentialeng
dc.subject.keywordAnalytic functionseng
dc.subject.keywordEspacios de Orliczspa
dc.subject.lembTEORÍA DE LA INFORMACIÓNspa
dc.subject.lembENTROPÍA (TEORÍA DE LA INFORMACIÓN)spa
dc.subject.lembESPACIOS DE BANACHspa
dc.subject.lembFÍSICA CUÁNTICAspa
dc.subject.lembANÁLISIS MATEMÁTICOspa
dc.subject.lembGEOMETRÍA DIFERENCIALspa
dc.subject.lembFUNCIONES ANALÍTICASspa
dc.titleA q-exponential statistical Banach manifoldeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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