Stable Decision Problems.
CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF STATISTICS
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A particular kind of continuity is studied, a kind judged important especially as a prologue to attempting elicitation of prior distributions and utility functions. There are other kinds of continuity that are alternatives to those chosen, and which also deserve study. Stability, as defined in this paper, offers the beginning of a Bayesian approach to robustness. On the real line, squared error loss is never stable, while absolute error is strongly stable for all opinions H. While the approach in this paper is more mathematical than some other approaches to robustness, which may be a disadvantage, it has the advantage of starting from a clear philosophical foundation, namely personalistic Bayesianism.
- Operations Research