Efficient Monte Carlo simulation via the generalized splitting method

Botev, Zdravko I.; Kroese, Dirk P.

doi:10.1007/s11222-010-9201-4

Cited by 92 publications

(88 citation statements)

References 25 publications

(33 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Good values can be estimated by an (independent) adaptive pilot algorithm, as explained in Section 5. In Botev and Kroese (2010), the authors typically use s = 10, so ρ t ≈ 1/10, but this choice is arbitrary and has no particular justification. Our empirical experiments with various choices of s (see Section 7)…”

Section: A Generalized Splitting Algorithmmentioning

confidence: 99%

“…The new method proposed here is an adaptation of the generalized splitting (GS) algorithm introduced by Botev and Kroese (2010), which is itself a modification of the classical multilevel splitting methodology for rare-event simulation (L'Ecuyer et al, 2009). The general idea of GS is to define a discrete-time Markov chain whose state (at any given step) represents a realization of the random variables involved in the simulation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Static Network Reliability Estimation via Generalized Splitting

Botev

L’Ecuyer

Rubino

et al. 2013

INFORMS Journal on Computing

Self Cite

View full text Add to dashboard Cite

We propose a novel simulation-based method that exploits a generalized splitting (GS) algorithm to estimate the reliability of a graph (or network), defined here as the probability that a given set of nodes are connected, when each link of the graph is failed with a given (small) probability. For large graphs, in general, computing the exact reliability is an intractable problem and estimating it by standard Monte Carlo methods poses serious difficulties, because the unreliability (one minus the reliability) is often a rare-event probability. We show that the proposed GS algorithm can accurately estimate extremely small unreliabilities and we exhibit large examples where it performs much better than existing approaches. It is also flexible enough to dispense with the frequently made assumption of independent edge failures.

show abstract

Section: A Generalized Splitting Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Static Network Reliability Estimation via Generalized Splitting

Botev

L’Ecuyer

Rubino

et al. 2013

INFORMS Journal on Computing

Self Cite

View full text Add to dashboard Cite

show abstract

“…Similar to randomized algorithms [12], [13] splitting algorithms explore the connection between counting and sampling problems and in particular the reduction from approximate counting of a discrete set to approximate sampling of elements of this set, where the sampling is performed by the classic MCMC method [18]. Very recently, [1] discusses several splitting variants in a very similar setting, including a discussion on an empirical estimate of the variance of the rare event probability estimate.…”

Section: Introduction: the Splitting Methodsmentioning

confidence: 99%

On the Use of Smoothing to Improve the Performance of the Splitting Method

Cérou¹,

Guyader²,

Rubinstein³

et al. 2011

Stochastic Models

View full text Add to dashboard Cite

We present an enhanced version of the splitting method, called the smoothed splitting method (SSM), for counting associated with complex 1 Corresponding author (http://iew3.technion.ac.il/Home/Users/ierrr01.phtml). 1 sets, such as the set defined by the constraints of an integer program and in particular for counting the number of satisfiability assignments. Like the conventional splitting algorithms, ours uses a sequential sampling plan to decompose a "difficult" problem into a sequence of "easy" ones. The main difference between SSM and splitting is that it works with an auxiliary sequence of continuous sets instead of the original discrete ones. The rationale of doing so is that continuous sets are easier to handle. We show that while the proposed method and its standard splitting counterpart are similar in their CPU time and variability, the former is more robust and more flexible than the latter.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Efficient Monte Carlo simulation via the generalized splitting method

Cited by 92 publications

References 25 publications

Static Network Reliability Estimation via Generalized Splitting

Static Network Reliability Estimation via Generalized Splitting

On the Use of Smoothing to Improve the Performance of the Splitting Method

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

Contact Info

Product

Resources

About