scholarly journals Multilevel Sequential Importance Sampling for Rare Event Estimation

2020 ◽  
Vol 42 (4) ◽  
pp. A2062-A2087 ◽  
Author(s):  
F. Wagner ◽  
J. Latz ◽  
I. Papaioannou ◽  
E. Ullmann
Keyword(s):  
Importance Sampling ◽  
Rare Event ◽  
Sequential Importance Sampling

scholarly journals Rare-Event Simulation of Heavy-Tailed Random Walks by Sequential Importance Sampling and Resampling

2012 ◽  
Vol 44 (04) ◽  
pp. 1173-1196
Author(s):  
Hock Peng Chan ◽  
Shaojie Deng ◽  
Tze-Leung Lai
Keyword(s):  
Random Walks ◽  
Importance Sampling ◽  
Rare Event ◽  
Sequential Importance Sampling ◽  
New Approach ◽  
Martingale Representation ◽  
Event Simulation ◽  
Markov Random ◽  
Heavy Tailed ◽  
Asymptotically Efficient

We introduce a new approach to simulating rare events for Markov random walks with heavy-tailed increments. This approach involves sequential importance sampling and resampling, and uses a martingale representation of the corresponding estimate of the rare-event probability to show that it is unbiased and to bound its variance. By choosing the importance measures and resampling weights suitably, it is shown how this approach can yield asymptotically efficient Monte Carlo estimates.

scholarly journals Rare-Event Simulation of Heavy-Tailed Random Walks by Sequential Importance Sampling and Resampling

2012 ◽  
Vol 44 (4) ◽  
pp. 1173-1196 ◽  
Author(s):  
Hock Peng Chan ◽  
Shaojie Deng ◽  
Tze-Leung Lai
Keyword(s):  
Random Walks ◽  
Importance Sampling ◽  
Rare Event ◽  
Sequential Importance Sampling ◽  
New Approach ◽  
Martingale Representation ◽  
Event Simulation ◽  
Markov Random ◽  
Heavy Tailed ◽  
Asymptotically Efficient

We introduce a new approach to simulating rare events for Markov random walks with heavy-tailed increments. This approach involves sequential importance sampling and resampling, and uses a martingale representation of the corresponding estimate of the rare-event probability to show that it is unbiased and to bound its variance. By choosing the importance measures and resampling weights suitably, it is shown how this approach can yield asymptotically efficient Monte Carlo estimates.

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.

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