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A Bayesian analysis of layered defense systems

Part of: Parametric inference Markov processes

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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