This monograph focuses on sequential analysis as applied to the problem of hypothesis testing and changepoint detection. General hypothesis testing deals with the problem of determining which of the given N hypotheses is true based on a given set of observations. In sequential hypothesis testing, testing is done as the observations arrive in sequence. Thus, the number of observations it takes to arrive at a decision is indeed random. In contrast, fixed sample size hypothesis testing involves decision making based on a fixed number of observations. The sequential hypothesis test on average requires less observations compared to the fixed sample size test for the same values of probability of miss and probability of false alarm. Because of this, property sequential tests are preferred over fixed sample size tests whenever there is a cost associated with the observations.

Changepoint detection, on the other hand, deals with the problem of identifying a change in hypothesis from one to another based on a given set of observations. Invariably, this change has to be detected quickly; therefore, changepoint detection problems are referred to as “quickest changepoint detection problems.” In quickest changepoint detection problems, the aim is to minimize the detection delay subject to a constraint on the probability of a false alarm. There are two different approaches to quickest changepoint detection: Bayesian and Minimax. In the Bayesian approach, the changepoint is assumed to be random; therefore, one can associate a distribution to the changepoint. On the other hand, in the Minimax approach, the changepoint is determined so that the worst-case detection delay is minimized. The well-known cumulative sum control chart (CUSUM) procedure is widely used for quickest changepoint detection because of its optimal nature with respect to the Minimax approach.

The application domains of hypothesis testing and changepoint detection problems range from mechanical engineering to computer science (CS) and engineering. For example, the quickest changepoint detection approach is used in quality control for the detection of disorders. Intrusion detection in the domain of computer network surveillance and security is another instance where the quickest changepoint detection approach is applied.

Tartakovsky et al. provide a holistic treatment on sequential hypothesis testing and changepoint detection by considering simple binary to multiple decision problems and different observation models, from the independent and identically distributed (IID) ones to non-IID ones (including state-space and hidden Markov models). The book also attempts to bring results (from different disciplines like statistics, applied probability, electrical engineering, and CS) pertaining to sequential hypothesis testing and changepoint detection under one proof. After the introductory two chapters (which provide an introduction to the book and the basics of probability, statistics, and hypothesis testing), the rest of the book is divided into three sections: “Sequential Hypothesis Testing,” “Changepoint Detection,” and “Applications.”

Section 1 comprises chapters 3 through 5. Chapter 3 considers binary hypothesis testing under the sequential framework. The contents include optimality of sequential probability ratio tests (SPRT), Wald’s approximations, and the handling of nuisance parameters in SPRT. Chapter 4 extends sequential binary hypothesis testing to include multiple simple hypotheses (in which the probability distribution of observations under the various competing hypotheses is completely specified). Chapter 5 extends sequential hypothesis testing to the case of composite hypotheses (in which the probability distribution of observations under the various competing hypotheses belongs to a class indexed by the unknown parameter).

Section 2 comprises chapters 6 to 10. Chapter 6 provides an introduction to changepoint models and the basic optimality criteria, namely Bayesian and Minimax, that are at the heart of changepoint detection problems. Chapters 7 and 8 discuss the Bayesian and Minimax sequential changepoint detection problems. Several theoretical results pertaining to Shiryaev and Shiryaev-Roberts procedures for the Bayesian case, and the CUSUM procedure and its optimality for the non-Bayesian case, are discussed here. Chapter 9 considers changepoint detection for the case of composite hypotheses, and chapter 10 discusses the problem of sequential changepoint detection and isolation. Chapter 11 presents select applications of the sequential hypothesis testing and changepoint detection problems in many diverse areas.

In conclusion, this monograph provides in-depth coverage of sequential hypothesis testing and changepoint techniques. Two other recent books on these topics [1,2] focus mainly on continuous-time models. This book adopts an approach based on discrete-time models, which is more suitable for practitioners in various areas. The authors also made a conscious effort of making the book self-contained by covering some of the basic material in chapter 2. This monograph is a must-read for all researchers who apply sequential hypothesis testing and the changepoint detection framework in the diverse areas of electrical engineering, mechanical/production engineering, and operations research.