Multi-variate quickest detection of significant change process

Szajowski, Krzysztof (2011): Multi-variate quickest detection of significant change process. Forthcoming in: Lecture Notes in Computer Science , Vol. 7037, No. GameSec 2011 (2011): pp. 56-66.

Abstract

The paper deals with a mathematical model of a surveillance system based on a net of sensors. The signals acquired by each node of the net are Markovian process, have two different transition probabilities, which depends on the presence or absence of a intruder nearby. The detection of the transition probability change at one node should be confirmed by a detection of similar change at some other sensors. Based on a simple game the model of a fusion center is then constructed. The aggregate function defined on the net is the background of the definition of a non-cooperative stopping game which is a model of the multivariate disorder detection

• Item Type: MPRA Paper
• Language: English
• Keywords: voting stopping rule, majority voting rule, monotone voting strategy, change-point problems, quickest detection, sequential detection, simple game
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General

References

Bojdecki, T.: Probability maximizing approach to optimal stopping and its application to a disorder problem. Stochastics 3, 61–71 (1979)

Brodsky, B., Darkhovsky, B.: Nonparametric Methods in Change-Point Problems, Mathematics and Its Applications, vol. 243. Kluwer Academic Publisher, Dordrecht (1993)

Domingos, P., Pazzani, M.: On the optimality of the simple bayesian classifier under zero-one loss. Machine Leaning 29, 103–130 (1997)

Dresher, M.: The mathematics of games of strategy. Theory and applications. Dover Publications, Inc., New York (1981)

Ferguson, T.S.: Selection by committee. In: Nowak, A., Szajowski, K. (eds.) Advances in Dynamic Games, Ann. Internat. Soc. Dynam. Games, vol. 7, pp. 203–209. Birkh ̈user, Boston (2005)

Gharehshiran, O.N., Krishnamurthy, V.: Coalition formation for bearings-only localization in sensor networks—a cooperative game approach. IEEE Trans. Signal Process. 58(8), 4322–4338 (2010)

Huang, Y.S., Suen, C.Y.: A method of combining multiple experts for recognition of unconstrained handwritten numerals. IEEE Transactions on Pattern Analysis and Machine Learning 17, 90–93 (1995)

Kang, H.J., Kim, K., Kim, J.H.: Optimal approximation of discrete probability distribution with kth-order dependency and its application to combining multiple classifiers. Pattern Recognition Letters 18, 515–523 (1997)

Kurano, M., Yasuda, M., Nakagami, J.: Multi-variate stopping problem with a majority rule. J. Oper. Res. Soc. Jap. 23, 205–223 (1980)

Lam, L., Krzyzak, A.: A theoretical analysis of the application of majority voting to pattern recognition, Jerusalem, Israel, pp. 418–420 (1994)

Lam, L., Suen, C.Y.: Application of majority voting to pattern recognition: An analysis of its behavior and performance. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 27(5), 533–568 (1997)

Merz, C.: Using correspondence analysis to combine classifiers. Machine Learning 36, 33–58 (1999)

Moulin, H.: Game Theory for the Social Sciences. New York University Press, New York (1986)

Nash, J.: Non-cooperative game. Annals of Mathematics 54(2), 286–295 (1951)

Owen, G.: Game theory, 3rd edn. Academic Press Inc., San Diego (1995)

Poor, V.H., Hadjiliadis, O.: Quickest detection. Cambridge University Press, Cambridge (2009)

Raghavan, V., Veeravalli, V.V.: Quickest change detection of a Markov process across a sensor array. IEEE Trans. Inform. Theory 56(4), 1961–1981 (2010)

Sarnowski, W., Szajowski, K.: Optimal detection of transition probability change in random sequence. Stochastics An International Journal of Probability and Stochastic Processes, 13 (First published on: March 10, 2011 (iFirst))

Shiryaev, A.: The detection of spontaneous effects. Sov. Math., Dokl. 2, 740–743 (1961)

Shiryaev, A.: Optimal Stopping Rules. Springer, Heidelberg (1978)

Szajowski, K.: Optimal on-line detection of outside observations. J. of Statistical Planning and Inference 30, 413–422 (1992)

Szajowski, K., Yasuda, M.: Voting procedure on stopping games of Markov chain. In: Christer, A.H., Osaki, S., Thomas, L.C. (eds.) UK-Japanese Research Workshop on Stochastic Modelling in Innovative Manufecuring, July 21-22, 1995. Lecture Notes in Economics and Mathematical Systems, vol. 445, pp. 68–80. Springer, Heidelberg (1996)

Tartakovsky, A.G., Rozovskii, B.L., Blaˇek, R.B., Kim, H.: Detection of intrusions in information systems by sequential change-point methods. Stat. Methodol. 3(3), 252–293 (2006)

Tartakovsky, A.G., Veeravalli, V.V.: Asymptotically optimal quickest change detection in distributed sensor systems. Sequential Anal. 27(4), 441–475 (2008)

Yasuda, M., Nakagami, J., Kurano, M.: Multi-variate stopping problem with a monoton rule. J. Oper. Res. Soc. Jap. 25, 334–350 (1982)

Yoshida, M.: Probability maximizing approach for a quickest detection problem with complocated Markov chain. J. Inform. Optimization Sci. 4, 127–145 (1983)