Sequential Monte Carlo for rare event estimation

Cérou, Frédéric; Moral, Pierre Del; Furon, Teddy; Guyader, Arnaud

doi:10.1007/s11222-011-9231-6

Cited by 161 publications

(220 citation statements)

References 23 publications

(23 reference statements)

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“…When the event {φ(X) < T } is rare relatively to the available simulation budget (which is often the case in safety and reliability issues), dierent algorithms described in [Sobol, 1994], [Bucklew, 2004], [Rubinstein and Kroese, 2004], [Zhang, 1996], [Bjerager, 1991], [Botev and Kroese, 2012], [Cérou et al, 2012] have notably been proposed to estimate accurately its probability.…”

Section: Debris Satellite Collision Simulationmentioning

confidence: 99%

Probabilistic Safety Analysis of the Collision Between a Space Debris and a Satellite with an Island Particle Algorithm

Vergé¹,

Mitard²,

Moral³

et al. 2016

Springer Optimization and Its Applications

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Collision between satellites and space debris seldom happens, but the loss of a satellite by collision may have catastrophic consequences both for the satellite mission and for the space environment. To support the decision to trigger o a collision avoidance manoeuver, an adapted tool is the determination of the collision probability between debris and satellite. This probability estimation can be performed with rare event simulation techniques when Monte Carlo techniques are not enough accurate. In this chapter, we focus on analyzing the inuence of dierent simulation parameters (such as the drag coecient) that are set for to simplify the simulation, on the collision probability estimation. A bad estimation of these simulation parameters can strongly modify rare event probability estimations. We design here a new island particle Markov chain Monte Carlo algorithm to determine the parameters that, in case of bad estimation, tend to increase the collision probability value. This algorithm also gives an estimate of the collision probability maximum taking into account the likelihood of the parameters. The principles of this statistical technique are described throughout this chapter.

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Section: Debris Satellite Collision Simulationmentioning

confidence: 99%

Probabilistic Safety Analysis of the Collision Between a Space Debris and a Satellite with an Island Particle Algorithm

Vergé¹,

Mitard²,

Moral³

et al. 2016

Springer Optimization and Its Applications

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“…Many Adaptive versions of the Multilevel Splitting approach have been proposed in the recent years, and are found with different names in the literature; see for instance [3], [20], [23], [22], [24] , [21], [34], [65], [64].…”

Section: Adaptive Multilevel Splitting Ideal Casementioning

confidence: 99%

Recent advances in various fields of numerical probability

et al. 2015

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Abstract. The goal of this paper is to present a series of recent contributions on some various problems of numerical probability. Beginning with the Richardson-Romberg Multilevel Monte-Carlo method which, among other fields of applications, is a very efficient method for the approximation of diffusion processes, we focus on some adaptive multilevel splitting algorithms for rare event simulation. Then, the third part is devoted to the simulation of McKean-Vlasov forward and decoupled forwardbackward stochastic differential equations by some cubature algorithms. Finally, we tackle the problem of the weak error estimation in total variation norm for a general Markov semi-group.

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“…The inequality for σ arises because the independence of initial states diminishes with increasing levels: unsuccessful traces are discarded and new initial states are drawn from successful traces. Several possibilities have been provided to minimise this dependence effect in [3]. In the following, for sake of simplicity, we assume that this goal is achieved.…”

Section: Fixed Level Algorithmmentioning

confidence: 99%

Importance Splitting for Statistical Model Checking Rare Properties

Jégourel

Legay

Sedwards

2013

Computer Aided Verification

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Statistical model checking avoids the intractable growth of states associated with probabilistic model checking by estimating the probability of a property from simulations. Rare properties are often important, but pose a challenge for simulation-based approaches: the relative error of the estimate is unbounded. A key objective for statistical model checking rare events is thus to reduce the variance of the estimator. Importance splitting achieves this by estimating a sequence of conditional probabilities, whose product is the required result. To apply this idea to model checking it is necessary to define a score function based on logical properties, and a set of levels that delimit the conditional probabilities. In this paper we motivate the use of importance splitting for statistical model checking and describe the necessary and desirable properties of score functions and levels. We illustrate how a score function may be derived from a property and give two importance splitting algorithms: one that uses fixed levels and one that discovers optimal levels adaptively.

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Sequential Monte Carlo for rare event estimation

Cited by 161 publications

References 23 publications

Probabilistic Safety Analysis of the Collision Between a Space Debris and a Satellite with an Island Particle Algorithm

Probabilistic Safety Analysis of the Collision Between a Space Debris and a Satellite with an Island Particle Algorithm

Recent advances in various fields of numerical probability

Importance Splitting for Statistical Model Checking Rare Properties

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