dc.contributor.author Van den Boogaart, Karl Gerard dc.contributor.author Egozcue Rubí, Juan José dc.contributor.author Pawlowsky-Glahn, Vera dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III dc.date.accessioned 2011-03-22T11:12:58Z dc.date.available 2011-03-22T11:12:58Z dc.date.created 2010-12 dc.date.issued 2010-12 dc.identifier.citation van den Boogaart, K.; Egozcue, J. J.; Pawlowsky-Glahn, V. Bayes linear spaces. "SORT: statistics and operations research transactions", Desembre 2010, vol. 34, núm. 2, p. 201-222. dc.identifier.issn 1696-2281 dc.identifier.uri http://hdl.handle.net/2117/12014 dc.description.abstract Linear spaces consisting of $\sigma$-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. dc.format.extent 22 p. dc.language.iso eng dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat dc.subject.lcsh Exponential families (Statistics) dc.subject.lcsh Probability measures dc.subject.lcsh Vector spaces dc.title Bayes linear spaces dc.type Article dc.subject.lemac Famílies exponencials (Estadística) dc.subject.lemac Probabilitats, Mesures de dc.subject.lemac Espais vectorials dc.contributor.group Universitat Politècnica de Catalunya. NRG - Riscos Naturals i Geoestadística dc.subject.ams Classificació AMS::60 Probability theory and stochastic processes::60A Foundations of probability theory dc.subject.ams Classificació AMS::62 Statistics::62E Distribution theory dc.relation.publisherversion http://www.idescat.cat/sort/sort342/34.2.4.boogaart-etal.pdf dc.rights.access Open Access drac.iddocument 5414782 dc.description.version Postprint (published version) upcommons.citation.author van den Boogaart, K.; Egozcue, J. J.; Pawlowsky-Glahn, V. upcommons.citation.published true upcommons.citation.publicationName SORT: statistics and operations research transactions upcommons.citation.volume 34 upcommons.citation.number 2 upcommons.citation.startingPage 201 upcommons.citation.endingPage 222
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