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Title:
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Evidence functions: a compositional approach to information
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Author:
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Egozcue Rubí, Juan José; Pawlowsky Glahn, Vera
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Other authors:
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Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. COSDA-UPC - COmpositional and Spatial Data Analysis |
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Abstract:
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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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Abstract:
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Peer Reviewed |
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Subject(s):
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-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 |
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Rights:
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Document type:
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Article - Submitted version
Article |
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Published by:
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Institut d'Estadística de Catalunya
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Share:
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