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Title: Conditional problem for objective probability (English)
Author: Kříž, Otakar
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 34
Issue: 1
Year: 1998
Pages: [27]-40
Summary lang: English
Category: math
Summary: Marginal problem (see [Kel]) consists in finding a joint distribution whose marginals are equal to the given less-dimensional distributions. Let’s generalize the problem so that there are given not only less-dimensional distributions but also conditional probabilities. It is necessary to distinguish between objective (Kolmogorov) probability and subjective (de Finetti) approach ([Col,Sco]). In the latter, the coherence problem incorporates both probabilities and conditional probabilities in a unified framework. Different algorithms available for its solution are described e. g. in ([Gil,Col,Vic]). In the context of the former approach, it will be shown that it is possible to split the task into solving the marginal problem independently and to subsequent solving pure “conditional" problem as certain type of optimization. First, an algorithm (Conditional problem) that generates a distribution whose conditional probabilities are equal to the given ones is presented. Due to the multimodality of the criterion function, the algorithm is only heuristical. Due to the computational complexity, it is efficient for small size problems e. g. 5 dichotomical variables. Second, a method is mentioned how to unite marginal and conditional problem to a more general consistency problem for objective probability. Due to computational complexity, both algorithms are effective only for limited number of variables and conditionals. The described approach makes possible to integrate in the solution of the consistency problem additional knowledge contained e. g. in an empirical distribution. (English)
Keyword: marginal problem
Keyword: algorithm
MSC: 60A99
MSC: 65C50
MSC: 68T30
MSC: 68T35
idZBL: Zbl 1274.60013
idMR: MR1619053
Date available: 2009-09-24T19:13:25Z
Last updated: 2015-03-27
Stable URL:
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