Bayes linear spaces

• Autores: Karl Gerald Van Den Boogaart, Juan José Egozcue Rubí , Vera Pawlowsky Glahn
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 34, Nº. 2, 2010, págs. 201-222
• Idioma: inglés
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• Dialnet Métricas: 1 Cita
• Resumen

  • 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.

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