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FIRST INTERNATIONAL
SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Ghent, Belgium

30 June - 2 July 1999

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** ELECTRONIC PROCEEDINGS **

## Paolo Vicig

# Epistemic Independence for Imprecise Probabilities

** Abstract **

The aim of this paper is that of studying a notion of independence for imprecise probabilities which is essentially based on the intuitive meaning of this concept. This is expressed, in the case of two events, by the reciprocal irrelevance of the knowledge of the value of each event for evaluating the other one, and has been termed epistemic independence. In order to consider more general situations in the framework of coherent imprecise probabilities, a definition of (epistemic) independence is introduced referring to arbitrary sets of logically independent partitions. Logical independence is viewed as a natural prerequisite for epistemic independence. It is then proved that the definition is always consistent, its relationship with the factorization rule is analysed, and some of its more relevant implications are discussed.

** Keywords. ** Coherent imprecise probabilities, (epistemic) independence, logical independence, factorization.

The paper is available in the following formats:

** Authors addresses: **

Paolo Vicig

Dipartimento di Matematica applicata "de Finetti"

Facolta' di Economia

Universita' di Trieste

Piazzale Europa, 1

I - 34127 Trieste, ITALY

fax: ++39 040 54209

phone: ++39 040 6767108

** E-mail addresses: **

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