Bayes linear spaces

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hdl:2099/11227
Document typeArticle
Defense date2010
PublisherInstitut d'Estadística de Catalunya
Rights accessOpen Access
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Abstract
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.
CitationVan den Boogaart, Karl Gerald; Egozcue, Juan José; Pawlowsky Glahn, Vera. Bayes linear spaces. "SORT", vol. 34, núm. 2, p. 201-222.
ISSN1696-2281
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