Sequential Analysis: Hypothesis Testing and Changepoint Detection.

摘要

The main focus of this book is on a systematic development of the theory of sequential hypothesis testing (Part I) and changepoint detection (Part II). In Part III, we briefly describe certain important applications where theoretical results can be used efficiently, perhaps with some reasonable modifications. We review recent accomplishments in hypothesis testing and changepoint detection both in decision-theoretic (Bayesian) and non-decision-theoretic (non-Bayesian) contexts. The emphasis is not only on more traditional binary hypotheses but also on substantially more difficult multiple decision problems. Scenarios with simple hypotheses and more realistic cases of (two and finitely many) composite hypotheses are considered and treated in detail. While our major attention is on more practical discrete-time models, since we strongly believe that life is discrete in nature??? (not only due to measurements obtained from devices and sensors with discrete sample rates), certain continuous-timemodels are also considered once in a while, especially when general results can be obtained very similarly in both cases. It should be noted that although we have tried to provide rigorous proofs of the most important results, in some cases we included heuristic argument instead of the real proofs as well as gave references to the sources where the proofs can be found.