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A Bayesian analysis of layered defense systems

Part of: Markov processes Parametric inference

Published online by Cambridge University Press:  14 July 2016

Dhaifalla K. Al-mutairi ,
Talal M. Al-khamis  and
Mohamed S. Abdel-Hameed
Dhaifalla K. Al-mutairi*
Affiliation:
Kuwait University
Talal M. Al-khamis*
Affiliation:
Kuwait University
Mohamed S. Abdel-Hameed*
Affiliation:
Kuwait University
*
∗Postal address for all authors: Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969 Safat, Kuwait 13060.
∗Postal address for all authors: Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969 Safat, Kuwait 13060.
∗Postal address for all authors: Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969 Safat, Kuwait 13060.
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Abstract

A Bayesian approach for analyzing layered defense systems is presented. This approach incorporates the dependence of penetration probabilities on the size of attackers going into any layer. A general formula is developed for computing the predictive distribution of the number of attackers surviving any layer as well as the posterior distribution of the penetration probabilities under the a priori assumptions that: (i) the probabilities are dependent and their joint distribution is Dirichlet, and (ii) the probabilities are independent. Positive dependence of the penetration probabilities as well as the number of attackers surviving the different layers is also established.

Keywords

ASSOCIATIONBAYESIAN STATISTICSDIRICHLET DISTRIBUTIONLAYERED DEFENSE SYSTEMSMULTIVARIATE TOTAL POSITIVITYTOTAL POSITIVITY

MSC classification

Primary: 62F15: Bayesian inference
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 449 - 457
Copyright
Copyright © Applied Probability Trust 1997 

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References

Abdel-Hameed, M. S. and Sampson, A. R. (1978) Positive dependence of the bivariate and trivariate absolute normal, t, χ 2, and F distributions. Ann. Statist. 6, 1360–1368.Google Scholar
Al-Mutairi, D. K. and Soland, R. M. (1992) A generalized layered defense model. ORSA TIMS meeting. November 1992, San Francisco.Google Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Block, H. W., Sampson, A. R. and Savits, T. H. (1991) Topics in Statistical Dependence. Institute of Mathematical Statistics, New York.Google Scholar
Bracken, J. H. (1986) Monte Carlo layered defense system model. IDA paper no. P-1966. Institute for Defense Analysis, Alexandria, VA.Google Scholar
Fang, K., Kotz, S. and Ng, K. (1990) Symmetric Multivariate and Related Distributions. Chapman and Hall, New York.Google Scholar
Karlin, S. (1968) Total Positivity. Stanford University Press, Stanford, CA.Google Scholar
Karlin, S. and Rinott, Y. (1980) Classes of ordering measures and related correlation inequalities I: multivariate totally positive distributions. J. Multivar. Anal. 10, 467–498.CrossRefGoogle Scholar
Nunn, W., Glass, D., Hsu, I. and Perin, D. (1982) Analysis of a layered defense model. Operat. Res. 30, 585–589.Google Scholar
Orlin, D. (1987) Optimal weapons allocation against layered defense. Naval Res. Logist. 34, 605–617.Google Scholar