Some Bayesian Learning Processes

摘要

The paper illustrates the technique of degradation as a method for the logical analysis of tasks. A well-defined decision task is degraded by eliminating certain knowledge of the prior probabilities, by delaying payoffs, by withholding knowledge of conditional probabilities, and finally by eliminating the sample data. In each case, a straightforward application of probability theory using Bayes theorem yields an optimal strategy. Each strategy is optimal in that it yields the largest possible total expected utility for repeated performances of the task. The resulting set of degradations is open to two interpretations. One interpretation is that each optimal strategy corresponds to the performance of an ideal decision maker operating under certain constraints. The other interpretation is that each degraded task corresponds to a possible laboratory experiment. In this case, the technique of degradation serves to introduce some structure into the relations between the possible experimental tasks. (Author)