Optimal Sequentially Planned Decision Procedures

Learning from experience, making decisions on the basis of the available information, and proceeding step by step to a desired goal are fundamental behavioural qualities of human beings. Nevertheless, it was not until the early 1940's that such a statistical theory - namely Sequential Analysis - was created, which allows us to investigate this kind of behaviour in a precise manner. A. Wald's famous sequential probability ratio test (SPRT; see example (1.8 turned out to have an enormous influence on the development of this theory. On the one hand, Wald's fundamental monograph 'Sequential Analysis' ([Wa]*) is essentially centered around this test. On the other hand, important properties of the SPRT - e.g. Bayes- optimality, minimax-properties, 'uniform' optimality with respect to expected sample sizes - gave rise to the development of a general statistical decision theory. As a conse- quence, the SPRT's played a dominating role in the further development of sequential analysis and, more generally, in theoretical statistics.