Independent products in infinite spaces
type: Item
instance of: scholarly article
title: Independent products in infinite spaces
zbMATH Open document ID: 1320.60008
author: Yong-Cai Geng
author: Sumit K. Garg
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-01-16T00:00:00Z
review text: Independence is a basic notion in many probabilistic models. In the case of imprecise probability there are various extensions of this notion. The paper analyzes the notion of independence of the assessment of mutual irrelevance between two variables. The authors show that, contrary to the case of finite spaces, the independent product that arises from two marginal using Walley's notion of coherence does not always exist. Since independent products do not exist in general, two alternative models that guarantee their existence are investigated. On the one hand, the notion of coherence proposed by \textit{P. M. Williams} [Int. J. Approx. Reasoning 44, No. 3, 366--383 (2007; Zbl 1114.60005)] is considered; on the other, a single assumption of irrelevance of one variable to the other is considered. In the last case, the extension to imprecision of the law of total probability can be used to establish the joint model. In addition, the strong product is characterized as the greatest factorizing product of two given marginals.
reviewed by: Ion Iancu
Mathematics Subject Classification ID: 60A99
zbMATH DE Number: 6387132
zbMATH Keywords: independence
zbMATH Keywords: irrelevance
zbMATH Keywords: imprecise probability
zbMATH Keywords: coherence
zbMATH Keywords: infinite spaces
zbMATH Keywords: factorisation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2014.12.049
OpenAlex ID: W2063418763
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DOI: 10.1016/J.JMAA.2014.12.049
description: scientific article; zbMATH DE number 6387132