Bayes linear spaces
Linear spaces consisting of $\sigma$-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 sp...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/12014 |
| Acceso en línea: | https://hdl.handle.net/2117/12014 |
| Access Level: | acceso abierto |
| Palabra clave: | Exponential families (Statistics) Probability measures Vector spaces Famílies exponencials (Estadística) Probabilitats, Mesures de Espais vectorials Classificació AMS::60 Probability theory and stochastic processes::60A Foundations of probability theory Classificació AMS::62 Statistics::62E Distribution theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat |
| Sumario: | Linear spaces consisting of $\sigma$-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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