Independent products in infinite spaces
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.
scientific article; zbMATH DE number 6387132
scientific article