Evidence functions: a compositional approach to information
The discrete case of Bayes’ formula is considered the paradigm of information acquisition. Prior and posterior probability functions, as well as likelihood functions, called evidence functions, are compositions following the Aitchison geometry of the simplex, and have thus vector character. Bayes’ f...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| 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:2117/178505 |
| Acceso en línea: | https://hdl.handle.net/2117/178505 |
| Access Level: | acceso abierto |
| Palabra clave: | Evidence function Bayes’ formula Aitchison geometry compositions orthonormal basis simplex scalar information Classificació AMS::60 Probability theory and stochastic processes::60A Foundations of probability theory Classificació AMS::60 Probability theory and stochastic processes::60E Distribution theory Classificació AMS::62 Statistics::62E Distribution theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica |
| Sumario: | The discrete case of Bayes’ formula is considered the paradigm of information acquisition. Prior and posterior probability functions, as well as likelihood functions, called evidence functions, are compositions following the Aitchison geometry of the simplex, and have thus vector character. Bayes’ formula becomes a vector addition. The Aitchison norm of an evidence function is introduced as a scalar measurement of information. A fictitious fire scenario serves as illustration. Two different inspections of affected houses are considered. Two questions are addressed: (a) which is the information provided by the outcomes of inspections, and (b) which is the most informative inspection. |
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