Summary

The book deals with the problems of sequential hypothesis testing, parameter estimation and simultaneous hypothesis testing and parameter estimation under conditions of complete and incomplete a priori information. Truncated and untruncated sequential procedures are optimized in Bayesian and non-Bayesian setting. Asymptotically optimal sequential tests for simple and composite hypotheses as well as optimal and almost optimal sequential procedures for detection of changes in distributions are determined. Various models of observations are considered: independent, identically distributed observations, nonhomogeneous and correlated processes with both discrete and continuous time parameter. Thus the book is concerned as with simple so with complex statistical models. It is important for numerous applications.

Considerable attention is paid to the comparison of sequential procedures with the best non-sequential ones. It is pointed out that sequential methods have sufficiently big advantage in different situations and under different conditions.

The primary goal of the book is to review recent developments in Sequential Analysis and to apply these developments to numerous practical problems in Bayesian and non-decision-theoretical contexts. The book combines the author's original results with critical survey of recent developments in the field.

In addition to theoretical concepts particular examples from different areas are discussed. In particular, special attention is paid to the questions of detecting signals with known and unknown appearance time and duration in the multichannel information systems.