Updating Sets of Probabilities

Abstract

There are several well-known justifications for conditioning as the appropriate method for updating a single probability measure, given an observation. However, there is a significant body of work arguing for sets of probability measures, rather than single measures, as a more realistic model of uncertainty. Conditioning still makes sense in this context--we can simply condition each measure in the set individually, then combine the results--and, indeed, it seems to be the preferred updating procedure in the literature. But how justified is conditioning in this richer setting? Here we show, by considering an axiomatic account of conditioning given by van Fraassen, that the single-measure and sets-of-measures cases are very different. We show that van Fraassen's axiomatization for the former case is nowhere near sufficient for updating sets of measures. We give a considerably longer (and not as compelling) list of axioms that together force conditioning in this setting, and describe other update methods that are allowed once any of these axioms is dropped.

In Proceedings of the Fourteenth Conference on Uncertainty in AI, 1998, pp. 173-182

References in corpus (2)

• A New Approach to Updating Beliefs
• Decision Making with Interval Influence Diagrams

Cited by in corpus (6)

• Probabilistic Belief Change: Expansion, Conditioning and Constraining
• On Stochastic Belief Revision and Update and their Combination
• A Game-Theoretic Analysis of Updating Sets of Probabilities
• A Game-Theoretic Analysis of Updating Sets of Probabilities
• Revising Incompletely Specified Convex Probabilistic Belief Bases
• Making Decisions Using Sets of Probabilities: Updating, Time Consistency, and Calibration