Forward irrelevance |
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Authors: | Gert de Cooman Enrique Miranda |
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Institution: | 1. Systems Research Group, Ghent University, Technologiepark—Zwijnaarde 914, 9052 Zwijnaarde, Belgium;2. Department of Statistics and Operations Research—‘Rey Juan Carlos University. C-Tulipán, s/n’, 28933 Móstoles, Spain |
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Abstract: | We investigate how to combine marginal assessments about the values that random variables assume separately into a model for the values that they assume jointly, when (i) these marginal assessments are modelled by means of coherent lower previsions and (ii) we have the additional assumption that the random variables are forward epistemically irrelevant to each other. We consider and provide arguments for two possible combinations, namely the forward irrelevant natural extension and the forward irrelevant product, and we study the relationships between them. Our treatment also uncovers an interesting connection between the behavioural theory of coherent lower previsions, and Shafer and Vovk's game-theoretic approach to probability theory. |
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Keywords: | 60A99 60G99 91A40 |
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