State-of-the-Art in Sequential Change-Point Detection

Methodology and Computing in Applied Probability

Volumn 14, Issue 3, 2012, Pages 649-684

  Polunchenko, Aleksey S ^a   Tartakovsky, Alexander G ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

CUSUM chart; Quickest change detection; Sequential analysis; Sequential change point detection; Shiryaev's procedure; Shiryaev Roberts procedure; Shiryaev Roberts Pollak procedure; Shiryaev Roberts r procedure

Indexed keywords

EID: 84864433151     PISSN: 13875841     EISSN: 15737713     Source Type: Journal    
DOI: 10.1007/s11009-011-9256-5     Document Type: Article

References (49)

1. Atkinson K, Han W (2009) Theoretical numerical analysis: a functional analysis framework. In: Texts in applied mathematics, vol 39, 3rd edn. Springer doi: 10. 1007/978-1-4419-0458-4.
2. Basseville M, Nikiforov IV (1993) Detection of abrupt changes: theory and application. Prentice Hall, Englewood Cliffs.
3. Brodsky BE, Darkhovsky BS (1993) Nonparameteric methods in change point problems. In: Mathematics and its applications, vol 243. Kluwer Academic Publishers.
4. Feinberg EA, Shiryaev AN (2006) Quickest detection of drift change for Brownian motion in generalized Bayesian and minimax settings. Stat Decis 24(4): 445-470. doi: 10. 1524/stnd. 2006. 24. 4. 445.
5. Ferguson TS (1967) Mathematical statistics-a decision theoretic approach. Academic Press, New York.
6. Fuh CD (2003) SPRT and CUSUM in hidden Markov models. Ann Stat 31(3): 942-977. doi: 10. 1214/aos/1056562468.
7. Fuh CD (2004) Asymptotic operating characteristics of an optimal change point detection in hidden Markov models. Ann Stat 32(5): 2305-2339. doi: 10. 1214/009053604000000580.
8. Girschick MA, Rubin H (1952) A Bayes approach to a quality control model. Ann Math Stat 23(1): 114-125. doi: 10. 1214/aoms/1177729489.
9. Harris TE (1963) The theory of branching processes. Springer-Verlag, Berlin.
10. Kesten H (1973) Random difference equations and renewal theory for products of random matrices. Acta Math. 131(1): 207-248. doi: 10. 1007/BF02392040.
11. Lai TL (1995) Sequential changepoint detection in quality control and dynamical systems. J R Stat Soc B 57(4): 613-658.
12. Lai TL (1998) Information bounds and quick detection of parameter changes in stochastic systems. IEEE Trans Inf Theory 44: 2917-2929. doi: 10. 1109/18. 737522.
13. Lorden G (1971) Procedures for reacting to a change in distribution. Ann Math Stat 42(6): 1897-1908.
14. Mevorach Y, Pollak M (1991) A small sample size comparison of the Cusum and the Shiryayev-Roberts approaches to changepoint detection. Am J Math Manage Sci 11: 277-298.
15. Moustakides GV (1986) Optimal stopping times for detecting changes in distributions. Ann Stat 14(4): 1379-1387.
16. Moustakides GV (2008) Sequential change detection revisited. Ann Stat 36(2): 787-807. doi: 10. 1214/009053607000000938.
17. Moustakides GV, Polunchenko AS, Tartakovsky AG (2011) A numerical approach to performance analysis of quickest change-point detection procedures. Stat Sin 21(2): 571-596.
18. Page ES (1954) Continuous inspection schemes. Biometrika 41(1): 100-115.
19. Pollak M (1985) Optimal detection of a change in distribution. Ann Stat 13(1): 206-227.
20. Pollak M (1987) Average run lengths of an optimal method of detecting a change in distribution. Ann Stat 15(2): 749-779.
21. Pollak M, Siegmund D (1986) Convergence of quasi-stationary to stationary distributions for stochastically monotone Markov processes. J Appl Probab 23(1): 215-220.
22. Pollak M, Tartakovsky AG (2009a) Asymptotic exponentiality of the distribution of first exit times for a class of Markov processes with applications to quickest change detection. Theory Probab Appl 53(3): 430-442.
23. Pollak M, Tartakovsky AG (2009b) Optimality properties of the Shiryaev-Roberts procedure. Stat Sin 19: 1729-1739.
24. Polunchenko AS, Tartakovsky AG (2010) On optimality of the Shiryaev-Roberts procedure for detecting a change in distribution. Ann Stat 36(6): 3445-3457. doi: 10. 1214/09-AOS775.
25. Poor HV, Hadjiliadis O (2008) Quickest detection. Cambridge University Press.
26. Ritov Y (1990) Decision theoretic optimality of the CUSUM procedure. Ann Stat 18(3): 1464-1469.
27. Roberts S (1966) A comparison of some control chart procedures. Technometrics 8(3): 411-430.
28. Shewhart WA (1931) Economic control of quality of manufactured product. D. van Nostrand Company, Inc., New York.
29. Shiryaev AN (1961) The problem of the most rapid detection of a disturbance in a stationary process. Sov Math Dokl 2: 795-799.
30. Shiryaev AN (1963) On optimum methods in quickest detection problems. Theory Probab Appl 8(1): 22-46. doi: 10. 1137/1108002.
31. Shiryaev AN (1978) Optimal stopping rules. Springer-Verlag, New York.
32. Shiryaev AN (2006) From disorder to nonlinear filtering and martingale theory. In: Bolibruch A, Osipov Y, Sinai Y (eds) Mathematical events of the twentieth century. Springer Berlin Heidelberg, pp 371-397, doi: 10. 1007/3-540-29462-7_18.
33. Shiryaev AN (2009) On the stochastic models and optimal methods in the quickest detection problems. Theory Probab Appl 53(3): 385-401. doi: 10. 1137/S0040585X97983717.
34. Shiryaev AN (2010) Quickest detection problems: fifty years later. Seq Anal 29: 345-385. doi: 10. 1080/07474946. 2010520580.
35. Siegmund D (1985) Sequential analysis: tests and confidence intervals. Springer Series in Statistics. Springer-Verlag, New York.
36. Springer MD, Thompson WE (1970) The distribution of products of Beta, Gamma and Gaussian random variables. SIAM J Appl math 18(4): 721-737. doi: 10. 1137/0118065.
37. Tartakovsky AG (1991) Sequential methods in the theory of information systems. Radio & Communications, Moscow, Russia.
38. Tartakovsky AG (2005) Asymptotic performance of a multichart CUSUM test under false alarm probability constraint. In: Proceedings of the 2005 IEEE Conference on Decision and Control, vol 44, pp 320-325.
39. Tartakovsky AG (2008) Discussion on "Is average run length to false alarm always an informative criterion?" by Yajun Mei. Seq Anal 27(4): 396-405. doi: 10. 1080/07474940802446046.
40. Tartakovsky AG (2009a) Asymptotic optimality in Bayesian changepoint detection problems under global false alarm probability constraint. Theory Probab Appl 53: 443-466. doi: 10. 1137/S0040585X97983754.
41. Tartakovsky AG (2009b) Discussion on "Optimal sequential surveillance for finance, public health, and other areas" by Marianne Frisén. Seq Anal 28(3): 365-371. doi: 10. 1080/07474940903041704.
42. Tartakovsky AG, Moustakides GV (2010) State-of-the-art in Bayesian changepoint detection. Seq Anal 29(2): 125-145. doi: 10. 1080/07474941003740997.
43. Tartakovsky AGPolunchenko AS (2010) Minimax optimality of the Shiryaev-Roberts procedure. In: Proceedings of the 5th international workshop on applied probability, Universidad Carlos III of Madrid, Spain.
44. Tartakovsky AG, Veeravalli VV (2005) General asymptotic Bayesian theory of quickest change detection. Theory Probab Appl 49(3): 458-497. doi: 10. 1137/S0040585X97981202.
45. Tartakovsky AG, Pollak M, Polunchenko AS (2008) Asymptotic exponentiality of first exit times for recurrent Markov processes and applications to changepoint detection. In: Proceedings of the 2008 International workshop on applied probability, Compiégne, France.
46. Tartakovsky AG, Polunchenko AS, Moustakides GV (2009) Design and comparison of Shiryaev-Roberts- and CUSUM-type change-point detection procedures. In: Proceedings of the 2nd International workshop in sequential methodologies, University of Technology of Troyes, Troyes, France.
47. Tartakovsky AG, Pollak M, Polunchenko AS (2011) Third-order asymptotic optimality of the generalized Shiryaev-Roberts changepoint detection procedures. Theoiya Veroyatnostej i ee Primeneniya 56(3) (in press).
48. Wald A (1947) Sequential analysis. J. Wiley & Sons, Inc., New York.
49. Woodroofe M (1982) Nonlinear renewal theory in sequential analysis. Society for Industrial and Applied Mathematics, Philadelphia, PA.