Probability Update: Conditioning vs. Cross-Entropy
Adam Grove, Joseph Halpern
Conditioning is the generally agreed-upon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of cross-entropy minimization, to handle updates that involve uncertain information. In this paper we re-examine such a case: van Fraassen's Judy Benjamin problem, which in essence asks how one might update given the value of a conditional probability. We argue that -- contrary to the suggestions in the literature -- it is possible to use simple conditionalization in this case, and thereby obtain answers that agree fully with intuition. This contrasts with proposals such as cross-entropy, which are easier to apply but can give unsatisfactory answers. Based on the lessons from this example, we speculate on some general philosophical issues concerning probability update.
Keywords: Cross-entropy, conditioning, probability update, Judy Benjamin
PS Link: HTTP://www.cs.cornell.edu/home/halpern/papers/jb.ps
PDF Link: /papers/97/p208-grove.pdf
AUTHOR = "Adam Grove
and Joseph Halpern",
TITLE = "Probability Update: Conditioning vs. Cross-Entropy",
BOOKTITLE = "Proceedings of the Thirteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-97)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1997",
PAGES = "208--214"