UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Algorithmic Learning in a Random World
Algorithmic Learning in a Random World
Inference with separately specified sets of probabilities in credal networks
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Updating sets of probabilities
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Artificial Intelligence
Safe probability: restricted conditioning and extended marginalization
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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We consider how an agent should update her beliefs when her beliefs are represented by a set P of probability distributions, 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 updating and calibration when uncertainty is described by sets of probabilities. Our results emphasize the key role of the rectangularity condition of Epstein and Schneider.