Optimal multistage sequential hypothesis testing

Abstract

This article deals with problems of sequential testing of two simple hypotheses about the distribution of a stochastic process. We consider sequential testing procedures with a finite maximum number (k, k≥2) of stages. Under some natural assumptions about the structure of the cost of observations, we describe the sequential procedures minimizing the average cost in the class of all k-stage sequential tests whose error probabilities do not exceed some prescribed levels. Bayesian tests are also considered. The results are applicable both to discrete and continuous-time stochastic processes. In the particular case of a Wiener process with a lineal drift, we evaluate the efficiency of optimal k-stage sequential tests with respect to the Wald’s SPRT and the Neyman-Pearson test, for k=2, 3 and 4 stages.