Statistics Seminars: Solving imprecise decision processes under act-state independence
2 November 2009 14:15 in CM221
The traditional approach to decision making relies on the use of (precise) probabilitilies to model uncertainty. More specifically, Russell and Norvig (1995) define decision theory as the association of probability theory and utility theory; the former to model uncertainty, and the latter to express preferences. However, it has been shown that many situations cannot be adequately represented by precise probability assessments, and the use of more general models has been advocated.
The goal of this presentation is to show the results obtained so far in our investigation of the conditions under which these general models can be applied to sequential decision making. In particular, we adopt arbitrary choice functions to obtain the main result, and later derive conditions under which this holds for imprecise probabilities. For illustrative purposes, we often refer to decision trees and Markov Decision Processes throughout our exposition. Assumptions are made, and in this initial study we restrict ourselves to the act-state indepenent case. Under these assumptions, we show that the sequential decision process can be optimally solved by considering a sequence of local, single staged problems. A simple coin tossing example is considered.
(This research is the result of collaboration with Matthias C. M. Troffaes and Nathan Huntly from Durham University)
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