The Goodman-Nguyen Relation within Imprecise Probability Theory

Abstract

The Goodman-Nguyen relation is a partial order generalising the implication (inclusion) relation to conditional events. As such, with precise probabilities it both induces an agreeing probability ordering and is a key tool in a certain common extension problem. Most previous work involving this relation is concerned with either conditional event algebras or precise probabilities. We investigate here its role within imprecise probability theory, first in the framework of conditional events and then proposing a generalisation of the Goodman-Nguyen relation to conditional gambles. It turns out that this relation induces an agreeing ordering on coherent or C-convex conditional imprecise previsions. In a standard inferential problem with conditional events, it lets us determine the natural extension, as well as an upper extension. With conditional gambles, it is useful in deriving a number of inferential inequalities.

Published version: http://www.sciencedirect.com/science/article/pii/S0888613X14001017

References in corpus (2)

• Quasi Conjunction, Quasi Disjunction, T-norms and T-conorms: Probabilistic Aspects
• Williams Coherence and Beyond

Cited by in corpus (5)

• Probabilities of conditionals and previsions of iterated conditionals
• Algebraic aspects and coherence conditions for conjoined and disjoined conditionals
• Probabilistic entailment and iterated conditionals
• 2-coherent and 2-convex Conditional Lower Previsions
• Weakly Consistent Extensions of Lower Previsions