In this paper, a nonadditive quantitative description of uncertain knowledge about statistical models is obtained by extending the likelihood function to sets and allowing the use of prior information. This description, which has the distinctive feature of not being calibrated, is called relative plausibility. It can be updated when new information is obtained, and it can be used for inference and decision making. As regards inference, the well-founded theory of likelihood-based statistical inference can be exploited, whereas decisions can be based on the minimax plausibility-weighted loss criterion. In the present paper, this decision criterion is introduced and some of its properties are studied, both from the conditional and from the repeated sampling point of view.
Keywords. Decision making, uncertainty, prior ignorance, minimax criterion, likelihood function, imprecise probabilities, nonadditive measure, completely maxitive measure, Shilkret integral, Choquet integral.
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Authors addresses:
Seminar für Statistik, LEO C13
ETH Zentrum
CH-8092 Zürich
E-mail addresses:
| Marco Cattaneo | cattaneo@stat.math.ethz.ch |