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Evidence functions: a compositional approach to information Egozcue Rubí, Juan José Pawlowsky Glahn, Vera Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental Universitat Politècnica de Catalunya. COSDA-UPC - COmpositional and Spatial Data Analysis Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant Probabilities Distribution (Probability theory) Evidence function Bayes' formula Aitchison geometry compositions orthonormal basis simplex scalar information Probabilitats Distribució (Teoria de la probabilitat) Classificació AMS::60 Probability theory and stochastic processes::60A Foundations of probability theory Classificació AMS::62 Statistics::62E Distribution theory 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. Peer Reviewed Postprint (author's final draft) 2018-07-01 Article Egozcue, J. J.; Pawlowsky, V. Evidence functions: a compositional approach to information. "SORT: statistics and operations research transactions", 1 Juliol 2018, vol. 42, núm. 2, p. 101-124. 1696-2281 https://hdl.handle.net/2117/129877 10.2436/20.8080.02.71 eng https://www.idescat.cat/sort/sort422/42.2.1.egozcue-pawlowsky.pdf Open Access 24 p. application/pdf Institut d'Estadística de Catalunya