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Bayes linear spaces

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van den Boogaart, Karl Gerald
Egozcue Rubí, Juan JoséMés informacióMés informacióMés informació
Pawlowsky Glahn, Vera
Document typeArticle
Defense date2010
PublisherInstitut d'Estadística de Catalunya
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
This work is protected by the corresponding intellectual and industrial property rights. Except where otherwise noted, its contents are licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
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. 
URIhttp://hdl.handle.net/2099/11227
ISSN1696-2281
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