An Efficient Simulation Method for Rare Events

Handle URI:
http://hdl.handle.net/10754/624084
Title:
An Efficient Simulation Method for Rare Events
Authors:
Rached, Nadhir B.; Benkhelifa, Fatma ( 0000-0003-1820-4207 ) ; Kammoun, Abla ( 0000-0002-0195-3159 ) ; Alouini, Mohamed-Slim ( 0000-0003-4827-1793 ) ; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. Closed-form expressions for the sum distribution do not generally exist, which has led to an increasing interest in simulation approaches. A crude Monte Carlo (MC) simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive, especially when dealing with rare events. Variance reduction techniques are alternative approaches that can improve the computational efficiency of naive MC simulations. We propose an Importance Sampling (IS) simulation technique based on the well-known hazard rate twisting approach, that presents the advantage of being asymptotically optimal for any arbitrary RVs. The wide scope of applicability of the proposed method is mainly due to our particular way of selecting the twisting parameter. It is worth observing that this interesting feature is rarely satisfied by variance reduction algorithms whose performances were only proven under some restrictive assumptions. It comes along with a good efficiency, illustrated by some selected simulation results comparing the performance of our method with that of an algorithm based on a conditional MC technique.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Issue Date:
7-Jan-2015
Type:
Poster
Appears in Collections:
Posters; Applied Mathematics and Computational Science Program; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

Full metadata record

DC FieldValue Language
dc.contributor.authorRached, Nadhir B.en
dc.contributor.authorBenkhelifa, Fatmaen
dc.contributor.authorKammoun, Ablaen
dc.contributor.authorAlouini, Mohamed-Slimen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-06-05T08:35:48Z-
dc.date.available2017-06-05T08:35:48Z-
dc.date.issued2015-01-07-
dc.identifier.urihttp://hdl.handle.net/10754/624084-
dc.description.abstractEstimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. Closed-form expressions for the sum distribution do not generally exist, which has led to an increasing interest in simulation approaches. A crude Monte Carlo (MC) simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive, especially when dealing with rare events. Variance reduction techniques are alternative approaches that can improve the computational efficiency of naive MC simulations. We propose an Importance Sampling (IS) simulation technique based on the well-known hazard rate twisting approach, that presents the advantage of being asymptotically optimal for any arbitrary RVs. The wide scope of applicability of the proposed method is mainly due to our particular way of selecting the twisting parameter. It is worth observing that this interesting feature is rarely satisfied by variance reduction algorithms whose performances were only proven under some restrictive assumptions. It comes along with a good efficiency, illustrated by some selected simulation results comparing the performance of our method with that of an algorithm based on a conditional MC technique.en
dc.titleAn Efficient Simulation Method for Rare Eventsen
dc.typePosteren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 6-9, 2015en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)en
dc.conference.locationKAUSTen
kaust.authorRached, Nadhir B.en
kaust.authorBenkhelifa, Fatmaen
kaust.authorKammoun, Ablaen
kaust.authorAlouini, Mohamed-Slimen
kaust.authorTempone, Raulen
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