Independent Natural Extension

We introduce a general definition for the independence of a number of finite-valued variables, based on coherent lower previsions. Our definition has an epistemic flavour: it arises from personal judgements that a number of variables are irrelevant to one another. We show that a number of already existing notions, such as strong independence, satisfy our definition. Moreover, there always is a least-committal independent model, for which we provide an explicit formula: the independent natural extension. Our central result is that the independent natural extension satisfies so-called marginalisation, associativity and strong factorisation properties. These allow us to relate our research to more traditional ways of defining independence based on factorisation. Key words: Epistemic irrelevance, epistemic independence, independent natural extension, strong product, factorisation. 1 Motivation In the literature on probability we can recognise two major approaches to defining indepe...

• Type: Conference
• Year: 2010
• Where: IPMU
• Authors: Gert de Cooman, Enrique Miranda, Marco Zaffalon
• Keywords: Epistemic, Epistemic Independence, Independent Natural Extension, Information Management, IPMU 2010