Updating Sets of Probabilities
Adam Grove, Joseph Halpern
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 Fraassens 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
Keywords: Conditioning, sets of probabilities, postulates.
PS Link: http://www.cs.cornell.edu/home/halpern/papers/bas.ps
PDF Link: /papers/98/p173-grove.pdf
AUTHOR = "Adam Grove
and Joseph Halpern",
TITLE = "Updating Sets of Probabilities",
BOOKTITLE = "Proceedings of the Fourteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-98)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1998",
PAGES = "173--182"