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Bayes linear spaces

Linear spaces consisting of σ-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

SORT : statistics and operations research transactions, 2010, vol. 34, núm. 4, p. 201-222

Institut d´Estadística de Catalunya (Idescat)

Autor: Van den Boogaart, Karl Gerald
Egozcue, Juan José
Pawlowsky-Glahn, Vera
Data: 2010
Resum: Linear spaces consisting of σ-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
Format: application/pdf
ISSN: 1696-2281 (versió paper)
2013-8830 (versió electrònica)
Accés al document: http://hdl.handle.net/10256/8996
Llenguatge: eng
Editor: Institut d´Estadística de Catalunya (Idescat)
Col·lecció: Reproducció digital del document publicat a: http://www.idescat.cat/sort/sort342/34.2.4.boogaart-etal.pdf
Articles publicats (D-IMA)
És part de: SORT : statistics and operations research transactions, 2010, vol. 34, núm. 4, p. 201-222
Drets: Attribution-NonCommercial-NoDerivs 3.0 Spain
URI Drets: http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Matèria: Espais vectorials
Vector spaces
Estadística bayesiana
Bayesian statistical decision theory
Banach, Espais de -- Propietat de Radon-Nikodym
Banach spaces -- Radon-Nikodym property
Anàlisi multivariable
Multivariate analysis
Títol: Bayes linear spaces
Tipus: info:eu-repo/semantics/article
Repositori: DUGiDocs

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