Likelihood-Based Statistical Decisions

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 likelihoodbased statistical inference can be exploited, whereas decisions can be based on the minimax plausibilityweighted 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