Stochastic Control and Numerical Methods with Applications to Communications. Game Theoretic/Subsolution to Importance Sampling for Rare Event Simulation

2008 ◽  
Author(s):  
Harold Kushner ◽  
Paul Dupuis
Keyword(s):  
Numerical Methods ◽  
Stochastic Control ◽  
Importance Sampling ◽  
Rare Event ◽  
Rare Event Simulation ◽  
Event Simulation ◽  
Game Theoretic

Estimation of cyber network risk using rare event simulation

2020 ◽  
pp. 154851292093455
Author(s):  
Alexander L Krall ◽  
Michael E Kuhl ◽  
Shanchieh J Yang
Keyword(s):  
Importance Sampling ◽  
Computational Simulation ◽  
Rare Event ◽  
Rare Event Simulation ◽  
Modeling And Analysis ◽  
Event Simulation ◽  
Importance Sampling Method ◽  
Statistical Inferences ◽  
Analysis Technique ◽  
Network Risk

Inherent vulnerabilities in a cyber network’s constituent machine services can be exploited by malicious agents. As a result, the machines on any network are at risk. Security specialists seek to mitigate the risk of intrusion events through network reconfiguration and defense. When dealing with rare cyber events, high-quality risk estimates using standard simulation approaches may be unattainable, or have significant attached uncertainty, even with a large computational simulation budget. To address this issue, an efficient rare event simulation modeling and analysis technique, namely, importance sampling for cyber networks, is developed. The importance sampling method parametrically amplifies certain aspects of the network in order to cause a rare event to happen more frequently. Output collected under these amplified conditions is then scaled back into the context of the original network to provide meaningful statistical inferences. The importance sampling methodology is tailored to cyber network attacks and takes the attacker’s successes and failures as well as the attacker’s targeting choices into account. The methodology is shown to produce estimates of higher quality than standard simulation with greater computational efficiency.

Bounded Relative Error Importance Sampling and Rare Event Simulation

2010 ◽  
Vol 40 (1) ◽  
pp. 377-398 ◽  
Author(s):  
Don L. McLeish
Keyword(s):  
Importance Sampling ◽  
Relative Error ◽  
Rare Event ◽  
Exponential Families ◽  
Cumulative Distribution ◽  
Rare Event Simulation ◽  
Tail Probabilities ◽  
Event Simulation ◽  
Tail Behaviour ◽  
Tail Events

AbstractWe consider estimating tail events using exponential families of importance sampling distributions. When the cannonical sufficient statistic for the exponential family mimics the tail behaviour of the underlying cumulative distribution function, we can achieve bounded relative error for estimating tail probabilities. Examples of rare event simulation from various distributions including Tukey's g&h distribution are provided.

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