Quickest detection problems: Fifty years later

Sequential Analysis

Volumn 29, Issue 4, 2010, Pages 345-385

  Shiryaev, Albert N ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

; , and CUSUM processes; Bayesian formulation; Brownian motion; Discrete time and G models; Disorder; Disruption; Free boundary problems; Minimax formulation; Multistage scheme and procedures; Quickest detection; Spontaneously appearing effects; Sufficient statistics

Indexed keywords

BAYESIAN FORMULATION; DISORDER; DISRUPTION; FREE-BOUNDARY PROBLEMS; MINIMAX; MULTISTAGE SCHEME AND PROCEDURES; QUICKEST DETECTION; SPONTANEOUSLY APPEARING EFFECTS; SUFFICIENT STATISTICS;

BAYESIAN NETWORKS; BROWNIAN MOVEMENT;

OPTIMIZATION;

EID: 78549254588     PISSN: 07474946     EISSN: 15324176     Source Type: Journal    
DOI: 10.1080/07474946.2010.520580     Document Type: Editorial

References (42)

1. Basseville, M. and Nikiforov, I. V. (1993). Detection of Abrupt Changes: Theory and Applications, Englewood Cliffs: PTR Prentice Hall.
2. Beibel, M. (1996). A Note on Ritov's Bayes Approach to the Minimax Property of the CUSUM Procedure, Annals of Statistics 24: 1804-1812.
3. Borovkov, A. A. (1972). Stochastic Processes in the Queueing Theory [Russian], Moscow: Nauka; English transl.: New York-Berlin: Springer-Verlag, 1976.
4. Burnaev, E. V., Feinberg, E. A., and Shiryaev, A. N. (2008). On the Asymptotic Optimality of Second Order in the Minimax Problem of the Quickest Detection of the Time of Change of Drift for Brownian Motion, Theory of Probability and Its Applications 53: 557-575.
5. Feinberg, E. A. and Shiryaev, A. N. (2006). Quickest Detection of Drift Change for Brownian motion in Generalized Bayesian and Minimax Settings, Statistics & Decisions 24: 445-470.
6. Frisén, M. (2007). Properties of Use of the Shewhart Method and Its Followers, Sequential Analysis 26: 171-193.
7. Hawkins, D. M. and Olwell, D. H. (1998). Cumulative Sum Charts and Charting for Quality Improvement, New York: Springer-Verlag.
8. Karlin, S. and Taylor, H. M. (1981). A Second Course in Stochastic Processes, New York: Academic Press.
9. Lorden, G. (1971). Procedures for Reacting to a Change in Distribution, Annals of Mathematical Statistics 42: 1897-1908.
10. Moustakides, G. V. (1986). Optimal Stopping Times for Detecting Changes in Distributions, Annals of Statistics 14: 1379-1387.
11. Moustakides, G. V. (2004). Optimality of the CUSUM Procedure in Continuous Time, Annals of Statistics 32: 302-315.
12. Nikiforov, I. V. (1995). A Generalized Change Detection Problem, IEEE Transactions on Information Theory 41: 171-187.
13. Nikiforov, I. V. (2003). A Lower Bound for the Detection/Isolation Delay in a Class of Sequential Tests, IEEE Transactions on Information Theory 49: 3037-3047.
14. Page, E. S. (1954). Continuous Inspection Schemes, Biometrika 41: 100-114.
15. Page, E. S. (1955). Control Charts with Warning Lines, Biometrika 42: 243-257.
16. Peskir, G. and Shiryaev, A. N. (2006). Optimal Stopping and Free-Boundary Problems, Basel: Birkhäuser.
17. Pollak, M. (1985). Optimal Detection of a Change in Distribution, Annals of Statistics 13: 206-227.
18. Pollak, M. and Siegmund, D. (1985). A Diffusion Process and Its Application to Detecting a Change in the Drift of Brownian Motion, Biometrika 72: 267-280.
19. Roberts, S. W. (1959). Control Charts Based on Geometric Moving Average, Technometrics 1: 239-250.
20. Roberts, S. W. (1966). A Comparison of Some Control Chart Procedures, Technometrics 8: 411-430.
21. Sequential Analysis (ed. N. Mukhopadhyay). Design Methods and Applications, 2007, vol. 26, issues 2, 3. Celebrating Eighty Years of Control Charts. Walter A. Shewhart's Legacy. Philadelphia, Taylor and Francis.
22. Shiryaev, A. N. (1961a). The Detection of Spontaneous Effects [Russian], Doklady Akademii Nauk SSSR 138: 799-801; English transl. in Soviet Mathematics. Doklady 2: 740-743.
23. Shiryaev, A. N. (1961b). The Problem of the Most Rapid Detection of a Disturbance of a Stationary Regime [Russian], Dokl. Akad. Nauk SSSR 138: 1039-1042; English transl. in Soviet Mathematics. Doklady 2: 795-799.
24. Shiryaev, A. N. (1963a). On Optimal Methods in Quickest Detection Problems [Russian], Teoriya Veroyatnostej i ee Primeneniya 8: 26-51; English transl. in Theory of Probability and Its Applications 8: 22-46.
25. Shiryaev, A. N. (1963b). On Detecting of Disorders in Industrial Processes. I [Russian], Teoriya Veroyatnostej i ee Primeneniya 8: 264-281; English transl. in Theory of Probability and Its Applications 8.
26. Shiryaev, A. N. (1963c). On Detecting of Disorders in Industrial Processes. II [Russian], Teoriya Veroyatnostej i ee Primeneniya 8: 431-443; English transl. in Theory of Probability and Its Applications 8.
27. Shiryaev, A. N. (1964a). Detection of Randomly Appearing Target in a Multichannel System [Russian], Trudy Matematicheskogo Instituta imeni V. A. Steklova 71: 113-117.
28. Shiryaev, A. N. (1964b). On Markov Sufficient Statistics in Nonadditive Bayes Problems of Sequential Analysis [Russian], Theory of Probability and Its Applications 9: 670-686; English transl. in Theory of Probability and Its Applications 9: 604-618.
29. Shiryaev, A. N. (1967). Two Problems of Sequential Analysis [Russian], Kibernetika (Kiev) 2: 79-86; English transl. in Cybernetics, 3: 63-69.
30. Shiryaev, A. N. (1976). Statistical Sequential Analysis, 2nd edition [Russian], Moscow: Nauka; English transl.: Optimal Stopping Rules, Applications of Mathematics 8, New York- Heidelberg: Springer-Verlag, 1978.
31. Shiryaev, A. N. (1996). Minimax Optimality of the Method Cumulative Sums (CUSUM) in the Case of Continuous Time, Uspekhi Matematicheskikh Nauk 51: 173-174; English transl. in Russian Mathematical Surveys 51: 750-751.
32. Shiryaev, A. N. (2002). Quickest Detection Problems in the Technical Analysis of the Financial Data, in Mathematical Finance-Bachelier Congress 2000: Selected Papers from the First World Congress of the Bachelier Finance Society (Paris, 2000), H. Geman et al., eds., pp. 487-521, Berlin: Springer-Verlag, Springer Finance.
33. Shiryaev, A. N. (2004). A Remark on the Quickest Detection Problems, Statistics & Decisions 22: 79-82.
34. Shiryaev, A. N. (2008a). On Stochastic Models and Optimal Methods in the Quickest Detection Problems, Theory of Probability and Its Applications 53: 417-436.
35. Shiryaev, A. N. (2008b). Generalized Bayesian Nonlinear Quickest Detection Problems: On Markov Family of Sufficient Statistics, in Mathematical Control Theory and Finance, pp. 377-386, Springer.
36. Shiryaev, A. N. and Leonov, V. (1959). On a Method of Calculation of Semi-invariants, Teoriya Veroyatnostej i ee Primeneniya 4: 341-355; English transl. in Theory of Probability and Its Applications 4: 319-329.
37. Shiryaev, A. N. and Zryumov, P. Y. (2009). On the Linear and Nonlinear Generalized Bayesian Disorder Problem (Discrete-Time Case), in Optimality and Risk-Modern Trends in Mathematical Finance. The Kabanov Festschrift, F. Delbaen, M. Rásonyi, and C. Stricker, eds., pp. 227-236, Berlin, Heidelberg: Springer-Verlag.
38. Tartakovsky, A. G. (1991). Sequential Methods in the Theory of Information Systems [Russian]. Moscow: Radio and Communications.
39. Tartakovsky, A. G. (2008). Asymptotic Optimality in Bayesian Change-Point Detection Problems Under Global False Alarm Probability Constraint, Theory of Probability and Its Applications 53: 472-499.
40. Tartakovsky, A. G. and Veeravalli, V. V. (2005). General Asymptotic Bayesian Theory of Quickest Change Detection, Theory of Probability and Its Applications 49: 458-497.
41. Theory of Probability and Its Applications, 2008, vol. 53, issue 3 (special issue on optimal stopping).
42. Wetherill, G. B. (1977). Sampling Inspection and Quality Control, London/New York: Chapman & Hall/Halsted Press