Evidence functions
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. Bay...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:200756 |
| Acesso em linha: | https://ddd.uab.cat/record/200756 https://dx.doi.org/urn:doi:10.2436/20.8080.02.71 |
| Access Level: | acceso abierto |
| Palavra-chave: | Evidence function Bayes' formula Aitchison geometry Compositions Orthonormal basis Simplex Scalar information |
| Resumo: | 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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