Independent Natural Extension for Infinite Spaces: Williams-Coherence to the Rescue

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Jasper De Bock ;
Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:121-132, 2017.

Abstract

We define the independent natural extension of two local models for the general case of infinite spaces, using both sets of desirable gambles and conditional lower previsions. In contrast to Miranda and Zaffalon (2015), we adopt Williams-coherence instead of Walley-coherence. We show that our notion of independent natural extension always exists—whereas theirs does not—and that it satisfies various convenient properties, including factorisation and external additivity.

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