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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)

Author: Boogaart, Karl Gerald van den
Egozcue, Juan José
Pawlowsky-Glahn, Vera
Date: 2010
Abstract: 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
Citation: 015158
ISSN: 1696-2281 (versió paper)
2013-8830 (versió electrònica)
Document access: http://hdl.handle.net/10256/8996
Language: eng
Publisher: Institut d´Estadística de Catalunya (Idescat)
Collection: Reproducció digital del document publicat a: http://www.idescat.cat/sort/sort342/34.2.4.boogaart-etal.pdf
Articles publicats (D-IMA)
Is part of: SORT : statistics and operations research transactions, 2010, vol. 34, núm. 4, p. 201-222
Rights: Attribution-NonCommercial-NoDerivs 3.0 Spain
Rights URI: http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Subject: 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
Title: Bayes linear spaces
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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