Sets of probability distributions, independence, and convexity

Fabio G. Cozman

Research output: Contribution to journalScientific reviewpeer-review

33 Scopus citations

Abstract

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of "strong independence" (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli's results and recent developments on the axiomatization of non-binary preferences, and its impact on "complete" independence, are described. © 2011 Springer Science+Business Media B.V.
Original languageAmerican English
Pages (from-to)577-600
Number of pages24
JournalSynthese
DOIs
StatePublished - 1 May 2012
Externally publishedYes

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