Bayes linear spaces
PublisherInstitut d'Estadística de Catalunya
Rights accessOpen Access
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.