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This book presents an overview of the diverse literature on change-point methodology and describes some unifying themes and recent breakthroughs. It can be used as a second-year Ph.D. level course in statistics. It is expected to be useful to researchers and graduate students, not only in statistics but also in engineering, biomedicine, economics and finance.
List of contents
Introduction. Statistical Quality Control and Fault Detection in Dynamical Systems. Change-Point Models and Segmentation. Kalman and Wonham Filters. Frequentist, Bayes and Empirical Bayes Approaches. Overview of Diverse Fields of Application. Basic Change-Point Methodology. Sequential Change-Point Detection. Page's Cusum Rule and Its Optimality Theory. Bayesian Formulation and the Shiryaev-Robert's Rule. Asymptotically Optimal Window-Limited Generalized Likelihood Ratio. Detection of Unknown Pre- and Post-Parameter Changes. Implementation. Fixed-Sample Change-Point Problems. Estimation and Testing of Single Change-Point. Likelihood and Bayesian Approaches to Multiple Change-Points. Bic, Modified Bic and Other Model Selection Criteria. Dynamic Programming and Segmentation. Bayesian Approach and Mcmc Implementation. Sequential Monte Carlo Methods. an Empirical Bayes Approach. Interplay Between Sequential and Fixed-Sample Problems. Alarm Signaling Time and Scan Statistics. Filtering and Smoothing in Hidden Markov Models. Multiple Change-Points and Sequential Surveillance. Applications to Engineering. on-Line Fault Detection and Diagnosis. Signal Detection and Target Tracking. Stochastic Control of Systems with Occasional Unknown Parameter Changes. Applications to Biology and Medicine. Analysis of Copy Number Variation (Cnv) Data. Circular Binary Segmentation. Stochastic Segmentation Models. Analysis of Next Generation Sequencing (Ngs) Data. Chip-Seq Data. Dna Methylation. Post-Marketing Pharmacovigilance and Surveillance in Public Health. Applications to Economics and Finance. Structural Changes in Econometric Time Series. Change-Point Models in Finance.
About the author
Tze Leung Lai is affiliated with the Department of Statistics, Stanford University. Haipeng Xing is affiliated with the Department of Applied Mathematics and Statistics, SUNY Stony Brook. Both Lai and Xing are well-known statisticians and have made a number of important contributions in the subject of change-point problems (including both theory and applications).
Summary
This book presents an overview of the diverse literature on change-point methodology and describes some unifying themes and recent breakthroughs. It can be used as a second-year Ph.D. level course in statistics. It is expected to be useful to researchers and graduate students, not only in statistics but also in engineering, biomedicine, economics and finance.
