This paper discusses fundamental aspects of inference with imprecise probabilities from the decision theoretic point of view. It is shown why the equivalence of prior risk and posterior loss, well known from classical Bayesian statistics, is no longer valid under imprecise priors. As a consequence, straightforward updating, as suggested by Walley's Generalized Bayes Rule or as usually done in the Robust Bayesian setting, may lead to suboptimal decision functions. As a result, it must be warned that, in the framework of imprecise probabilities, updating and optimal decision making do no longer coincide.
Keywords. Decision making, generalized risk, generalized expected loss, imprecise prior risk and posterior loss, robust Bayesian analysis, Generalized Bayes rule
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Ludwigstr. 33
D-80539 Munich
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E-mail addresses:
| Thomas Augustin | thomas@stat.uni-muenchen.de |
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