Unbiasedness of some generalized adaptive multilevel splitting algorithms

Bréhier, Charles-Édouard; Gazeau, Maxime; Goudenège, Ludovic; Lelièvre, Tony; Rousset, Mathias

doi:10.1214/16-aap1185

Cited by 45 publications

(106 citation statements)

References 38 publications

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“…Further theoretical and numerical investigations are contained in [14], especially in higher dimensional situations. The algorithm requires to use an importance function ξ taking values in R: the unbiasedness holds independently of the choice of ξ, but it is an open important question to study its impact on the efficiency.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

Recent advances in various fields of numerical probability

et al. 2015

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“…This version of the AMS is a variant of the algorithm that perfectly fits the theoretical frame from [3], so that the estimator of the rare event occurrence probability introduced in the following is unbiased.…”

Section: Mathematical Settingmentioning

confidence: 99%

“…The mathematical proofs of the unbiasedness and consistency of the AMS estimator are not presented in this paper. We refer the reader to [2] and [3] for theoretical support. At each iteration q ≥ 0, the level Z q+1 is chosen in such a way that the probability for a path X j q to have an importance greater than Z q+1 (i.e.…”

Section: Interpretation Of the Replicas Weightsmentioning

confidence: 99%

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Adaptive multilevel splitting for Monte Carlo particle transport

Louvin

Dumonteil

Lelièvre

et al. 2017

EPJ Nuclear Sci. Technol.

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Abstract. In the Monte Carlo simulation of particle transport, and especially for shielding applications, variance reduction techniques are widely used to help simulate realisations of rare events and reduce the relative errors on the estimated scores for a given computation time. Adaptive Multilevel Splitting (AMS) is one of these variance reduction techniques that has recently appeared in the literature. In the present paper, we propose an alternative version of the AMS algorithm, adapted for the first time to the field of particle transport. Within this context, it can be used to build an unbiased estimator of any quantity associated with particle tracks, such as flux, reaction rates or even non-Boltzmann tallies like pulse-height tallies and other spectra. Furthermore, the efficiency of the AMS algorithm is shown not to be very sensitive to variations of its input parameters, which makes it capable of significant variance reduction without requiring extended user effort.

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“…More recently, a new method called Adaptive Multilevel Splitting (or AMS) has been proposed by Cérou and Guyader [2], and studied in a more general setting by Bréhier et al [3]. This method also aims to duplicate the interesting particles of the simulation, but uses the knowledge accumulated during the simulation itself to determin on the fly which particle should be duplicated and at which point.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Multilevel Splitting for Monte Carlo particle transport

et al. 2017

Self Cite

View full text Add to dashboard Cite

Abstract. In the Monte Carlo simulation of particle transport, and especially for shielding applications, variance reduction techniques are widely used to help simulate realisations of rare events and reduce the relative errors on the estimated scores for a given computation time. Adaptive Multilevel Splitting is one of these variance reduction techniques that has recently appeared in the literature. In the present paper, we propose an alternative version of the AMS algortihm, adapted for the first time to the field of particle tranport. Within this context, it can be used to build an unbiased estimator of any quantity associated with particle tracks, such as flux, reaction rates or even non-Boltzmann tallies. Furthermore, the efficiency of the AMS algorithm is shown not to be very sensitive to variations of its input parameters, which makes it capable of significant variance reduction without requiring extended user effort.

show abstract

Unbiasedness of some generalized adaptive multilevel splitting algorithms

Cited by 45 publications

References 38 publications

Recent advances in various fields of numerical probability

Recent advances in various fields of numerical probability

Adaptive multilevel splitting for Monte Carlo particle transport

Adaptive Multilevel Splitting for Monte Carlo particle transport

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