Uncertainty in Artificial Intelligence
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Updating Probabilities
Peter Grunwald, Joseph Halpern
As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a ``naive space', which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR (coarsening at random) in the statistical literature characterizes when ``naive' conditioning in a naive space works. We show that the CAR condition holds rather infrequently. We then consider more generalized notions of update such as Jeffrey conditioning and minimizing relative entropy (MRE). We give a generalization of the CAR condition that characterizes when Jeffrey conditioning leads to appropriate answers, but show that there are no such conditions for MRE. This generalizes and interconnects previous results obtained in the literature on CAR and MRE.
Pages: 187-196
PS Link: http://www.cs.cornell.edu/home/halpern/papers/uai02.ps
PDF Link: /papers/02/p187-grunwald.pdf
AUTHOR = "Peter Grunwald and Joseph Halpern",
TITLE = "Updating Probabilities",
BOOKTITLE = "Proceedings of the Eighteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-02)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2002",
PAGES = "187--196"

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