证据功能:信息的合成方法

IF 0.7 4区数学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Sort-Statistics and Operations Research Transactions Pub Date : 2018-07-01 DOI:10.2436/20.8080.02.71

J. Egozcue, V. Pawlowsky-Glahn

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引用次数: 9

摘要

贝叶斯公式的离散情况被认为是信息获取的范例。先验和后验概率函数，以及被称为证据函数的似然函数，是遵循单纯形的艾奇逊几何的组合，因此具有矢量特性。贝叶斯公式变成了向量加法。引入证据函数的艾奇逊范数作为信息的标量度量。一个虚构的火灾场景可以作为说明。考虑对受影响房屋进行两种不同的检查。这里讨论了两个问题:(a)哪些是视察结果提供的资料，以及(b)哪些是资料最多的视察。

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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’ 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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来源期刊

Sort-Statistics and Operations Research Transactions 管理科学-统计学与概率论

CiteScore

3.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： SORT (Statistics and Operations Research Transactions) —formerly Qüestiió— is an international journal launched in 2003. It is published twice-yearly, in English, by the Statistical Institute of Catalonia (Idescat). The journal is co-edited by the Universitat Politècnica de Catalunya, Universitat de Barcelona, Universitat Autonòma de Barcelona, Universitat de Girona, Universitat Pompeu Fabra i Universitat de Lleida, with the co-operation of the Spanish Section of the International Biometric Society and the Catalan Statistical Society. SORT promotes the publication of original articles of a methodological or applied nature or motivated by an applied problem in statistics, operations research, official statistics or biometrics as well as book reviews. We encourage authors to include an example of a real data set in their manuscripts.