Sequential detection and identification of a change in the distribution of a Markov-modulated random sequence

IEEE Transactions on Information Theory

Volumn 55, Issue 7, 2009, Pages 3323-3345

  Dayanik, Savas ^a   Goulding, Christian ^a  

^a Princeton University   (United States)

Author keywords

Hidden Markov models; Optimal stopping; Sequential change detection; Sequential hypothesis testing

Indexed keywords

BAYESIAN; CHANGE DETECTION; DISCRETE-TIME; HYPOTHESIS TESTING; IDENTIFICATION PROBLEM; OPTIMAL DECISIONS; OPTIMAL STOPPING; OPTIMALITY; RANDOM SEQUENCE; SEQUENTIAL ANALYSIS; SEQUENTIAL CHANGE DETECTION; SEQUENTIAL DETECTION; SEQUENTIAL HYPOTHESIS TESTING; STATISTICAL DEPENDENCIES; UNOBSERVABLE;

COMPUTATIONAL GRAMMARS; CONTINUOUS TIME SYSTEMS; OBJECT RECOGNITION; OPTIMIZATION; RISK PERCEPTION; SIGNAL DETECTION;

HIDDEN MARKOV MODELS;

EID: 67650178793     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2021382     Document Type: Article

References (36)

1. K. J. Arrow, D. Blackwell, and M. A. Girshick, "Bayes and minimax solutions of sequential decision problems," Econometrica, vol. 17, pp. 213-244, 1949.
2. S. Asmussen, O. Nerman, and M. Olsson, "Fitting phase-type distributions via theEMalgorithm," Scand. J. Stat., vol. 23, no. 4, pp. 419-441, 1996.
3. M. Baron and A. G. Tartakovsky, "Asymptotic optimality of change-point detection schemes in general continuous-time models," Sequential Anal., vol. 25, no. 3, pp. 257-296, 2006.
4. M. Basseville and I. V. Nikiforov, Detection of Abrupt Changes: Theory and Application, ser. Prentice Hall Information and System Sciences Series. Englewood Cliffs, NJ: Prentice Hall, 1993.
5. A. Bobbio, A. Horváth, M. Scarpa, and M. Telek, "Acyclic discrete phase type distributions: Properties and a parameter estimation algorithm," Perform. Eval., vol. 54, no. 1, pp. 1-32, 2003.
6. R. J. Bolton and D. J. Hand, "Statistical fraud detection: A review," Statist. Sci., vol. 17, no. 3, pp. 235-249, 2002.
7. Y. S. Chow, H. Robbins, and D. Siegmund, Great Expectations: The Theory of Optimal Stopping. Boston, MA: Houghton Mifflin, 1971.
8. E. Çinlar, Introduction to Stochastic Processes. Englewood Cliffs, N.J: Prentice-Hall, 1975.
9. M. J. Crowder, Classical Competing Risks. London, U.K.: Chapman & Hall/CRC Press, 2001.
10. S. Dayanik, C. Goulding, and H. V. Poor, "Bayesian sequential change diagnosis," Math. Oper. Res., vol. 33, no. 2, pp. 475-496, 2008.
11. V. P. Dragalin, A. G. Tartakovsky, and V. V. Veeravalli, "Multihypothesis sequential probability ratio tests. I. asymptotic optimality," IEEE Trans. Inf. Theory, vol. 45, no. 7, pp. 2448-2461, Nov. 1999.
12. V. P. Dragalin, A. G. Tartakovsky, and V. V. Veeravalli, "Multihypothesis sequential probability ratio tests. II. Accurate asymptotic expansions for the expected sample size," IEEE Trans. Inf. Theory, vol. 46, no. 4, pp. 1366-1383, Jul. 2000.
13. C.-D. Fuh, "SPRT and CUSUM in hidden Markov models," Ann. Statist vol. 31, no. 3, pp. 942-977, 2003.
14. P. Hackl and A. H.Westlund, "Statistical analysis of structural change: An annotated bibliography," Emp. Econ., vol. 14, no. 2, pp. 167-92, 1989.
15. G. Horton and C. Isensee, "Approximation of discrete phase-type distributions," in Proc. 38th Annu. Simulations Symp., 2005.
16. A. Horváth and M. Telek, "Phfit: A general phase-type fitting tool," in Proc. 12th Performance TOOLS, 2002, pp. 82-91.
17. M. A. Johnson and M. R. Taaffe, "The Denseness of Phase Distributions," School of Industrial Eng., Purdue Univ., West Lafayette, IN, Res. Memo. 88-20, 1988.
18. T. L. Lai, "Sequential change-point detection in quality control and dynamical systems," J. Roy. Statist. Soc. Ser. B, vol. 57, no. 4, pp. 613-658, 1995.
19. T. L. Lai, "Sequential multiple hypothesis testing and efficient fault detection-isolation in stochastic systems," IEEE Trans. Inf. Theory vol. 46, no. 2, pp. 595-608, Mar. 2000.
20. T. L. Lai, "Sequential analysis: Some classical problems and new challenges," Statist. Sinica, vol. 11, no. 2, pp. 303-408, 2001.
21. G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, ser. ASA-SIAM Series on Statistics and Applied Probability. Philadelphia, PA: SIAM, 1999.
22. G. Lorden, "Procedures for reacting to a change in distribution," Ann. Math. Statist, vol. 42, pp. 1897-1908, 1971.
23. D. J. C. MacKay, Information Theory, Inference & Learning Algorithms Cambridge, U.K.: Cambridge Univ. Press, 2002.
24. G. V. Moustakides, "Optimal stopping times for detecting changes in distributions," Ann. Statist, vol. 14, no. 4, pp. 1379-1387, 1986.
25. M. F. Neuts, Liber Amicorum Prof. Emeritus H. Florin. Louvain, Belgium: Univ. Louvain, 1975, ch. Probability distributions of phase type, pp. 173-206.
26. M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models. New York: Dover, 1994.
27. I. V. Nikiforov, "A generalized change detection problem," IEEE Trans. Inf. Theory, vol. 41, no. 1, pp. 171-187, Jan. 1995.
28. I. V. Nikiforov, "A simple recursive algorithm for diagnosis of abrupt changes in random signals," IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2740-2746, Nov. 2000.
29. I. V. Nikiforov, "A lower bound for the detection/isolation delay in a class of sequential tests," IEEE Trans. Inf. Theory, vol. 49, no. 11, pp. 3037-3047, Nov. 2003.
30. T. Oskiper and H. V. Poor, "Online activity detection in a multiuser environment using the matrix cusum algorithm," IEEE Trans. Inf. Theory, vol. 48, no. 2, pp. 477-493, Feb. 2002.
31. M. Pollak, "Optimal detection of a change in distribution," Ann. Statist, vol. 13, no. 1, pp. 206-227, 1985.
32. A. N. Shiryayev, Optimal Stopping Rules. New York: Springer-Verlag, 1978, vol. 8.
33. A. G. Tartakovsky, "Multidecision quickest changepoint detection: previous achievements and open problems," Sequential Anal., vol. 27, pp. 201-231, 2008.
34. A. G. Tartakovsky and V. V. Veeravalli, "General asymptotic Bayesian theory of quickest change detection," Teor. Veroyatn. Primen., vol. 49, no. 3, pp. 538-582, 2004.
35. A. Wald and J. Wolfowitz, "Bayes solutions of sequential decision problems," Ann. Math. Statist., vol. 21, pp. 82-99, 1950.
36. B. Yakir, "Optimal detection of a change in distribution when the observations form a Markov chain with a finite state space," in Change-Point Problems (South Hadley, MA, 1992), ser. IMS Lecture Notes Monogr. Hayward, CA: Inst. Math. Statist., 1994, vol. 23, pp. 346-358.