An overview of importance splitting for rare event simulation

Mitard, J.; Pastel, Rudy; Gland, François Le

doi:10.1088/0143-0807/31/5/028

Cited by 25 publications

(20 citation statements)

References 17 publications

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“…The splitting technique builds up a nested hierarchy of events, where the event of interest contains the previous ones, cf., e.g. [1][2][3]. In the simulation conditional probabilities are estimated.…”

Section: Introductionmentioning

confidence: 99%

Patchwork sampling of stochastic differential equations

Kürsten

Behn

2016

Phys. Rev. E

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We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The method is based on a complete, nonoverlapping partition of the state space into patches on which the stochastic process is ergodic. On each of these patches we run simulations of the process strictly truncated to the corresponding patch, which allows effective simulations also in rarely visited regions. The correct weight for each patch is obtained by counting the attempted transitions between all different patches. The results are patchworked to cover the whole state space. We extend the concept of truncated Markov chains which is originally formulated for processes which obey detailed balance to processes not fulfilling detailed balance. The method is illustrated by three examples, describing the one-dimensional diffusion of an overdamped particle in a double-well potential, a system of many globally coupled overdamped particles in double-well potentials subject to additive Gaussian white noise, and the overdamped motion of a particle on the circle in a periodic potential subject to a deterministic drift and additive noise. In an appendix we explain how other well-known Markov chain Monte Carlo algorithms can be related to truncated Markov chains.

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Section: Introductionmentioning

confidence: 99%

Patchwork sampling of stochastic differential equations

Kürsten

Behn

2016

Phys. Rev. E

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“…[6,7,34]). The splitting algorithm used in this paper is completely described in [35]. In the present paper, we just recall the different notations and the principle of this algorithm.…”

Section: Adaptive Importance Splitting Techniquementioning

confidence: 99%

“…In the present paper, we just recall the different notations and the principle of this algorithm. For more details, one can consult [35].…”

Section: Adaptive Importance Splitting Techniquementioning

confidence: 99%

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Recommendations for the tuning of rare event probability estimators

Balesdent

Mitard

Marzat

2015

Reliability Engineering & System Safety

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a b s t r a c tBeing able to accurately estimate rare event probabilities is a challenging issue in order to improve the reliability of complex systems. Several powerful methods such as importance sampling, importance splitting or extreme value theory have been proposed in order to reduce the computational cost and to improve the accuracy of extreme probability estimation. However, the performance of these methods is highly correlated with the choice of tuning parameters, which are very difficult to determine. In order to highlight recommended tunings for such methods, an empirical campaign of automatic tuning on a set of representative test cases is conducted for splitting methods. It allows to provide a reduced set of tuning parameters that may lead to the reliable estimation of rare event probability for various problems. The relevance of the obtained result is assessed on a series of real-world aerospace problems.

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“…The particle filter method also relates to the importance splitting method (see, e.g., L'Ecuyer et al [18], Glasserman et al [12], Lagnoux [17], Morio et al [20]) to obtain the …”

Section: Uses For Simulationmentioning

confidence: 99%

Particle Methods for Data-Driven Simulation and Optimization

Birge¹

2012

2012 TutORials in Operations Research

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Please scroll down for article-it is on subsequent pagesINFORMS is the largest professional society in the world for professionals in the fields of operations research, management science, and analytics. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org INFORMS 2012 c 2012 INFORMS | isbn 978-0-9843378-3-5 http://dx.Abstract Particle methods provide a robust methodology for estimation and prediction. They can also apply to traditional operations research areas by, for example, providing an effective alternative for constructing Monte Carlo simulations of various systems and for dynamic optimization. This tutorial explains the fundamental ideas behind particle methods and how to use them in typical operations research contexts.

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An overview of importance splitting for rare event simulation

Cited by 25 publications

References 17 publications

Patchwork sampling of stochastic differential equations

Patchwork sampling of stochastic differential equations

Recommendations for the tuning of rare event probability estimators

Particle Methods for Data-Driven Simulation and Optimization

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