Bayes linear spaces

Linear spaces consisting of -finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of...

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Autores: van den Boogaart, Karl Gerald, Egozcue Rubí, Juan José|||0000-0002-5144-4483, Pawlowsky Glahn, Vera
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2099/11227
Acceso en línea:https://hdl.handle.net/2099/11227
Access Level:acceso abierto
Palabra clave:Probabilities
Aitchison geometry
Compositional data
Exponential families
Likelihood functions
Probability measures
Radon-Nikodym derivative
Probabilitats
Classificació AMS::60 Probability theory and stochastic processes::60A Foundations of probability theory
Classificació AMS::62 Statistics::62E Distribution theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística aplicada
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spelling Bayes linear spacesvan den Boogaart, Karl GeraldEgozcue Rubí, Juan José|||0000-0002-5144-4483Pawlowsky Glahn, VeraProbabilitiesAitchison geometryCompositional dataExponential familiesLikelihood functionsProbability measuresRadon-Nikodym derivativeProbabilitatsClassificació AMS::60 Probability theory and stochastic processes::60A Foundations of probability theoryClassificació AMS::62 Statistics::62E Distribution theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Estadística aplicadaLinear spaces consisting of -finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended.Peer ReviewedInstitut d'Estadística de Catalunya20102010-01-0120112011-10-28journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2099/11227reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2099/112272026-05-27T15:37:01Z
dc.title.none.fl_str_mv Bayes linear spaces
title Bayes linear spaces
spellingShingle Bayes linear spaces
van den Boogaart, Karl Gerald
Probabilities
Aitchison geometry
Compositional data
Exponential families
Likelihood functions
Probability measures
Radon-Nikodym derivative
Probabilitats
Classificació AMS::60 Probability theory and stochastic processes::60A Foundations of probability theory
Classificació AMS::62 Statistics::62E Distribution theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística aplicada
title_short Bayes linear spaces
title_full Bayes linear spaces
title_fullStr Bayes linear spaces
title_full_unstemmed Bayes linear spaces
title_sort Bayes linear spaces
dc.creator.none.fl_str_mv van den Boogaart, Karl Gerald
Egozcue Rubí, Juan José|||0000-0002-5144-4483
Pawlowsky Glahn, Vera
author van den Boogaart, Karl Gerald
author_facet van den Boogaart, Karl Gerald
Egozcue Rubí, Juan José|||0000-0002-5144-4483
Pawlowsky Glahn, Vera
author_role author
author2 Egozcue Rubí, Juan José|||0000-0002-5144-4483
Pawlowsky Glahn, Vera
author2_role author
author
dc.subject.none.fl_str_mv Probabilities
Aitchison geometry
Compositional data
Exponential families
Likelihood functions
Probability measures
Radon-Nikodym derivative
Probabilitats
Classificació AMS::60 Probability theory and stochastic processes::60A Foundations of probability theory
Classificació AMS::62 Statistics::62E Distribution theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística aplicada
topic Probabilities
Aitchison geometry
Compositional data
Exponential families
Likelihood functions
Probability measures
Radon-Nikodym derivative
Probabilitats
Classificació AMS::60 Probability theory and stochastic processes::60A Foundations of probability theory
Classificació AMS::62 Statistics::62E Distribution theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística aplicada
description Linear spaces consisting of -finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-01-01
2011
2011-10-28
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2099/11227
url https://hdl.handle.net/2099/11227
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Institut d'Estadística de Catalunya
publisher.none.fl_str_mv Institut d'Estadística de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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