Decision making under incomplete data using the imprecise Dirichlet model

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, including missing data. We derive efficient algorithms and discuss properties of the optimal solutions with respect to several criteria, including Gammamaximinity and E-admissibility. In the case of precise data and pure actions the former surprisingly leads us 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. We also briefly glance at the representation invariance principle (RIP) in the context of decision making.