This research involves a theory for making a sequence of selections from a number of stochastic processes. The selection made at each stage can depend on information regarding the various processes that has accummulated to that stage; that is, the decision problem is sequential. The project deals with four specific problems: (1) Finding the strategies that behave well over a large class of discount sequences and prior distributions, (2) Allocating experiments to groups of experimental units in stages, (3) Maximizing the probability of a particular number of successes, and (4) Allocating to one of two independent processes or to a third process that is the simultaneous application of the two independent processes. This research is in the general area of statistical decision theory. It has relevance to a variety of other scientific fields including economics, psychology, medicine, and engineering.
