A q-exponential statistical Banach manifold

Letµbe 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 ex...

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Autores:
Quiceno Echavarría, Héctor Román
Loaiza Ossa, Gabriel Ignacio
Tipo de recurso:
Fecha de publicación:
2013
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
eng
OAI Identifier:
oai:repository.eafit.edu.co:10784/5245
Acceso en línea:
http://hdl.handle.net/10784/5245
Palabra clave:
TEORÍA DE LA INFORMACIÓN
ENTROPÍA (TEORÍA DE LA INFORMACIÓN)
ESPACIOS DE BANACH
FÍSICA CUÁNTICA
ANÁLISIS MATEMÁTICO
GEOMETRÍA DIFERENCIAL
FUNCIONES ANALÍTICAS
Information theory
Entropy (information theory)
Banach spaces
Quantum physical
Mathematical analysis
Geometry, differential
Analytic functions
Espacios de Orlicz
Rights
License
Copyright © 2012 Elsevier Ltd. All rights reserved.
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repository_id_str
spelling 2015-04-24T16:18:49Z2013-022015-04-24T16:18:49ZG. 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)0022-247Xhttp://hdl.handle.net/10784/524510.1016/j.jmaa.2012.08.046Letµbe 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 functionLetµbe 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 functionengELSEVIERJournal of Mathematical Analysis and Applications Volume 398, Issue 2, 15 February 2013, Pages 466–476http://dx.doi.org/10.1016/j.jmaa.2012.08.046Copyright © 2012 Elsevier Ltd. All rights reserved.Acceso restringidohttp://purl.org/coar/access_right/c_16ecA q-exponential statistical Banach manifoldarticleinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionpublishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1TEORÍA DE LA INFORMACIÓNENTROPÍA (TEORÍA DE LA INFORMACIÓN)ESPACIOS DE BANACHFÍSICA CUÁNTICAANÁLISIS MATEMÁTICOGEOMETRÍA DIFERENCIALFUNCIONES ANALÍTICASInformation theoryEntropy (information theory)Banach spacesQuantum physicalMathematical analysisGeometry, differentialAnalytic functionsEspacios de Orliczdepartment:Universidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y AplicacionesHéctor R. Quiceno (hquiceno@eafit.edu.co)Gabriel Loaiza (gloaiza@eafit.edu.co)Quiceno Echavarría, Héctor RománLoaiza Ossa, Gabriel IgnacioAnálisis Funcional y AplicacionesJournal of Mathematical Analysis and Applications3982476466LICENSElicense.txtlicense.txttext/plain; charset=utf-82556https://repository.eafit.edu.co/bitstreams/f55bb6a4-b52b-4cf5-983a-79795e400512/download76025f86b095439b7ac65b367055d40cMD51ORIGINAL2013.pdf2013.pdfapplication/pdf282428https://repository.eafit.edu.co/bitstreams/8a011e8a-26d5-4ef6-bb0c-37e6c407dab3/downloade3b76444d8a3ca93f9f4565f6ee07c07MD5210784/5245oai:repository.eafit.edu.co:10784/52452021-09-24 16:44:19.487restrictedhttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co
dc.title.eng.fl_str_mv A q-exponential statistical Banach manifold
title A q-exponential statistical Banach manifold
spellingShingle A q-exponential statistical Banach manifold
TEORÍA DE LA INFORMACIÓN
ENTROPÍA (TEORÍA DE LA INFORMACIÓN)
ESPACIOS DE BANACH
FÍSICA CUÁNTICA
ANÁLISIS MATEMÁTICO
GEOMETRÍA DIFERENCIAL
FUNCIONES ANALÍTICAS
Information theory
Entropy (information theory)
Banach spaces
Quantum physical
Mathematical analysis
Geometry, differential
Analytic functions
Espacios de Orlicz
title_short A q-exponential statistical Banach manifold
title_full A q-exponential statistical Banach manifold
title_fullStr A q-exponential statistical Banach manifold
title_full_unstemmed A q-exponential statistical Banach manifold
title_sort A q-exponential statistical Banach manifold
dc.creator.fl_str_mv Quiceno Echavarría, Héctor Román
Loaiza Ossa, Gabriel Ignacio
dc.contributor.department.none.fl_str_mv department:Universidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y Aplicaciones
dc.contributor.eafitauthor.spa.fl_str_mv Héctor R. Quiceno (hquiceno@eafit.edu.co)
Gabriel Loaiza (gloaiza@eafit.edu.co)
dc.contributor.author.none.fl_str_mv Quiceno Echavarría, Héctor Román
Loaiza Ossa, Gabriel Ignacio
dc.contributor.researchgroup.spa.fl_str_mv Análisis Funcional y Aplicaciones
dc.subject.lemb.spa.fl_str_mv TEORÍA DE LA INFORMACIÓN
ENTROPÍA (TEORÍA DE LA INFORMACIÓN)
ESPACIOS DE BANACH
FÍSICA CUÁNTICA
ANÁLISIS MATEMÁTICO
GEOMETRÍA DIFERENCIAL
FUNCIONES ANALÍTICAS
topic TEORÍA DE LA INFORMACIÓN
ENTROPÍA (TEORÍA DE LA INFORMACIÓN)
ESPACIOS DE BANACH
FÍSICA CUÁNTICA
ANÁLISIS MATEMÁTICO
GEOMETRÍA DIFERENCIAL
FUNCIONES ANALÍTICAS
Information theory
Entropy (information theory)
Banach spaces
Quantum physical
Mathematical analysis
Geometry, differential
Analytic functions
Espacios de Orlicz
dc.subject.keyword.eng.fl_str_mv Information theory
Entropy (information theory)
Banach spaces
Quantum physical
Mathematical analysis
Geometry, differential
Analytic functions
dc.subject.keyword.spa.fl_str_mv Espacios de Orlicz
description Letµbe 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 function
publishDate 2013
dc.date.issued.none.fl_str_mv 2013-02
dc.date.available.none.fl_str_mv 2015-04-24T16:18:49Z
dc.date.accessioned.none.fl_str_mv 2015-04-24T16:18:49Z
dc.type.eng.fl_str_mv article
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
publishedVersion
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.local.spa.fl_str_mv Artículo
status_str publishedVersion
dc.identifier.citation.spa.fl_str_mv G. 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)
dc.identifier.issn.spa.fl_str_mv 0022-247X
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10784/5245
dc.identifier.doi.none.fl_str_mv 10.1016/j.jmaa.2012.08.046
identifier_str_mv G. 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)
0022-247X
10.1016/j.jmaa.2012.08.046
url http://hdl.handle.net/10784/5245
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.ispartof.spa.fl_str_mv Journal of Mathematical Analysis and Applications Volume 398, Issue 2, 15 February 2013, Pages 466–476
dc.relation.uri.none.fl_str_mv http://dx.doi.org/10.1016/j.jmaa.2012.08.046
dc.rights.spa.fl_str_mv Copyright © 2012 Elsevier Ltd. All rights reserved.
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
dc.rights.local.spa.fl_str_mv Acceso restringido
rights_invalid_str_mv Copyright © 2012 Elsevier Ltd. All rights reserved.
Acceso restringido
http://purl.org/coar/access_right/c_16ec
dc.publisher.spa.fl_str_mv ELSEVIER
institution Universidad EAFIT
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repository.name.fl_str_mv Repositorio Institucional Universidad EAFIT
repository.mail.fl_str_mv repositorio@eafit.edu.co
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