Optimal Sequentially Planned Decision Procedures PDF

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.