Quickest Detection
The problem of detecting abrupt changes in the behavior of an observed signal or time series arises in a variety of fields, including climate modeling, finance, image analysis, and security. Quickest detection refers to real-time detection of such changes as quickly as possible after they occur. Using the framework of optimal stopping theory, this book describes the fundamentals underpinning the field, providing the background necessary to design, analyze, and understand quickest detection algorithms. For the first time the authors bring together results which were previously scattered across disparate disciplines, and provide a unified treatment of several different approaches to the quickest detection problem. This book is essential reading for anyone who wants to understand the basic statistical procedures for change detection from a fundamental viewpoint, and for those interested in theoretical questions of change detection. It is ideal for graduate students and researchers of engineering, statistics, economics, and finance.
Why Read This Book
You should read Quickest Detection if you need a rigorous, unified foundation for detecting abrupt changes in real time — the book teaches you how to formulate change problems, derive optimal detection rules, and evaluate their performance using optimal stopping and sequential analysis. You will learn both Bayesian and minimax approaches and see how core procedures (CUSUM, Shiryaev, Shiryaev–Roberts) arise and perform in applications from radar and communications to finance and quality control.
Who Will Benefit
Graduate students, researchers, and practicing engineers in signal processing, communications, radar, finance, and security who need to design or analyze real-time change-point detection algorithms.
Level: Advanced — Prerequisites: Solid undergraduate/graduate-level probability and stochastic processes (including conditional expectation and martingales), basic statistical signal processing and hypothesis testing, and familiarity with calculus and linear algebra.
Key Takeaways
- Formulate quickest detection problems under Bayesian and minimax criteria and translate real-world tasks into sequential decision problems.
- Derive and implement canonical procedures such as CUSUM, Shiryaev, and Shiryaev–Roberts and understand their operating characteristics.
- Analyze detection delay and false-alarm tradeoffs using optimal stopping theory and asymptotic performance bounds.
- Model continuous- and discrete-time change scenarios (e.g., Gaussian, Poisson, Brownian cases) and select appropriate detectors.
- Apply performance evaluation techniques (average run length, Lorden and Pollak metrics) and design detectors to meet constraints.
- Extend single-stream results to multi-stream and networked sensing contexts and understand practical application implications for radar, communications, and monitoring systems.
Topics Covered
- 1. Introduction and motivation: quick detection problems and applications
- 2. Mathematical preliminaries: probability, stopping times, martingales
- 3. Bayesian formulation of quickest detection
- 4. Minimax and Lorden/Pollak criteria
- 5. Classical detection procedures: CUSUM, Page's test
- 6. Shiryaev and Shiryaev–Roberts procedures
- 7. Continuous-time models: Brownian and Poisson change models
- 8. Asymptotic optimality and performance bounds
- 9. Multi-stream and decentralized detection
- 10. Numerical methods and implementation issues
- 11. Applications: radar, communications, finance, environmental monitoring
- 12. Extensions, open problems, and references
Languages, Platforms & Tools
How It Compares
Covers similar theoretical ground to Basseville & Nikiforov's Detection of Abrupt Changes but places greater emphasis on optimal stopping, Bayesian/minimax formulations, and asymptotic optimality; more mathematical and probabilistic than classic engineering treatments like Wald's Sequential Analysis.
