Universiteit van Amsterdam

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Institute for Logic, Language and Computation

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6 November 2003, CWI INS4 seminar, Peter Grunwald

Speaker: Peter Grunwald (CWI)
Title: Updating Probabilities
Date: Thursday 6 November 2003
Time: 16:00
Location: CWI, Kruislaan 413c, room C001

(joint work with Joe Halpern, Cornell University, Ithaca, NY)
As examples such as the Monty Hall and the 3-prisoners 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. We give a detailed explanation of this phenomenon. A criterion known as CAR (``coarsening at random'') in the statistical literature characterizes when ``naive'' conditioning in a naive space works. We provide two new characterizations of CAR. First we show that in many situations, CAR essentially *cannot* hold, so that naive conditioning must give the wrong answer. Second, we provide a procedural characterization of CAR, giving a randomized algorithm that generates all and only distributions for which CAR holds. Both results complement earlier work by Gill, van der Laan and Robins.

We also 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, and show that there exist some very simple settings in which MRE essentially never gives the right results. This generalizes and interconnects previous results obtained in the literature on CAR and MRE.

Please note that this newsitem has been archived, and may contain outdated information or links.