Szajowski, Krzysztof (2011): Multivariate quickest detection of significant change process. Forthcoming in: Lecture Notes in Computer Science , Vol. 7037, No. GameSec 2011 (2011): pp. 5666.

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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 noncooperative stopping game which is a model of the multivariate disorder detection
Item Type:  MPRA Paper 

Original Title:  Multivariate quickest detection of significant change process 
Language:  English 
Keywords:  voting stopping rule, majority voting rule, monotone voting strategy, changepoint 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 
Item ID:  33838 
Depositing User:  Krzysztof Szajowski 
Date Deposited:  03. Oct 2011 01:47 
Last Modified:  16. Feb 2013 08:37 
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 ChangePoint 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 zeroone 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 bearingsonly 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 kthorder dependency and its application to combining multiple classifiers. Pattern Recognition Letters 18, 515–523 (1997) Kurano, M., Yasuda, M., Nakagami, J.: Multivariate 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 CyberneticsPart 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.: Noncooperative 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 online 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.) UKJapanese Research Workshop on Stochastic Modelling in Innovative Manufecuring, July 2122, 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 changepoint 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.: Multivariate 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) 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/33838 