Statistical methods work on a given number of observations or a fixed sample size for processing. Sequential analysis deals with the runtime observations or the dynamic sample size for the processing of data. Thus, a sequential analysis method depends on two rules: a stopping rule and a decision rule, having the choice to stop the observation process or to wait for another observation and, after stopping the observation, specifying estimation, detection, classification, and other operations on the data. This book discusses two theoretical tracks and several applications of sequential analysis.
The first two chapters discuss the motivation for sequential analysis methods with some selected applications and brief background about probability and statistics, respectively. The rest of the chapters are spread over three parts: “Sequential Hypothesis Testing,” “Change-Point Detection,” and “Applications.” The next three chapters detail the two simple, multiple simple, and composite hypotheses, respectively. Part 2 spans five chapters, covering changepoint detection. It handles problem formulations and optimality criteria in statistical models with changes, Bayesian and non-Bayesian approaches for sequential change detection, multichart changepoint detection procedures for composite hypotheses and multipopulation models, and sequential change detection and isolation. Part 3 uses examples to show readers how sequential analysis is implemented. These examples cover such topics as radio-navigation integrity monitoring using a toy example, vibration-based structural health monitoring, and intrusion detection in computer networks.
The authors also present typical monitoring application examples like civil infrastructure integrity, flight flutter, and mechanical system integrity, as well as applications in other areas: quality control, target detection and tracking, signal processing, finance, and economics. The experimental results of the changepoint detection methods are worth studying for those who tend to implement sequential methods in their observations and statistical analyses.
The description of both the extended and asymptotic optimality of the sequential probability ratio test in the general non-independent and identically distributed (non-IID) case makes this book an interesting read.
