PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

A Game-Theoretic Characterization of Updating Sets of Probabilities
Peter Grünwald and Joe Halpern


We consider how an agent should update her uncertainty when it is represented by a set \P of probability distributions and the agent observes that a random variable X takes on value x, given that the agent makes decisions using the minimax criterion, perhaps the best-studied and most commonly-used criterion in the literature. We adopt a game-theoretic framework, where the agent plays against a bookie, who chooses some distribution from \P. We consider two reasonable games that differ in what the bookie knows when he makes his choice. Anomalies that have been observed before, like time inconsistency, can be understood as arising because different games are being played, against bookies with different information. We characterize the important special cases in which the optimal decision rules according to the minimax criterion amount to either conditioning or simply ignoring the information. Finally, we consider the relationship between conditioning and calibration when uncertainty is described by sets of probabilities.

EPrint Type:Other
Additional Information:This paper was published on the CORR archive. It will be submitted to a conference/journal at a later date.
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:3328
Deposited By:Peter Grünwald
Deposited On:07 February 2008