The paper presents an efficient solution to decision problems where direct partial information on the distribution of the states of nature is available, either by observations of previous repetitions of the decision problem or by direct expert judgements.\\ To process this information we use a recent generalization of Walley's imprecise Dirichlet model, allowing us also to handle incomplete observations or imprecise judgements. We derive efficient algorithms and discuss properties of the optimal solutions. In the case of precise data and pure actions we are surprisingly led to a frequency-based variant of the Hodges-Lehmann criterion, which was developed in classical decision theory as a compromise between Bayesian and minimax procedures.
Keywords. Belief functions, coarse data, decision making, Hodges-Lehmann criterion, imperfect measurements, imprecise Dirichlet model, imprecise probabilities, incomplete data, interval probability, interval statistical models, predictive probabilities, set-valued observations, statistical data,
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Authors addresses:
Lev Utkin
Department of Computer Science,
St. Petersburg Forest Technical Academy
Institutski per. 5,
St. Petersburg, 194021
Thomas Augustin
Department of Statistics
University of Munich
Ludwigstr. 33
D-80539 Munich
Germany
E-mail addresses:
| Lev Utkin | lvu@utkin.usr.etu.spb.ru |
| Thomas Augustin | thomas@stat.uni-muenchen.de |