A survey of rare event simulation methods for static input–output models

Abstract

International audienceCrude Monte-Carlo or quasi Monte-Carlo methods are well suited to characterize events of which associated probabilities are not too low with respect to the simulation budget. For very seldom observed events, such as the collision probability between two aircraft in airspace, these approaches do not lead to accurate results. Indeed, the number of available samples is often insufficient to estimate such low probabilities (at least 10^6 samples are needed to estimate a probability of order 10^-4with 10% relative error with Monte-Carlo simulations). In this article, one reviewed different appropriate techniques to estimate rare event probabilities that require a fewer number of samples. These methods can be divided into four main categories: parameterization techniques of probability density function tails, simulation techniques such as importance sampling or importance splitting, geometric methods to approximate input failure space and finally, surrogate modeling. Each technique is detailed, its advantages and drawbacks are described and a synthesis that aims at giving some clues to the following question is given: “which technique to use for which problem?”

On the Efficient Simulation of the Distribution of the Sum of Gamma–Gamma Variates With Application to the Outage Probability Evaluation Over Fading Channels

“…From the above expression, we can see that the choice of Ω 0, in (20) will lead to reducing the variance as η 0 → 0.…”

“…where (18) where Ω 0, is given by (20). Thus, the IS estimator (7) has a bounded relative error when the conditions min…”

“…of the order of 10 −8 ), for which the MC method is inaccurate if the sample size is not large enough [20]. In fact, a naive MC estimator, based on a reasonably limited number of simulation runs, may provide irrelevant results.…”

Evaluation of failure probability under parameter epistemic uncertainty: application to aerospace system reliability assessment

“…Finally, estimating such a failure probability can be achieved using one of the classical methods available in the structural reliability literature [22]. To do so, two distinct classes of methods have been developed: approximation methods such as the FirstOrder Reliability Method (FORM) and the Second-Order Reliability Method (SORM), which both rely on the concept of Most-Probable Point (MPP); and simulation methods based on Monte Carlo simulations [21].…”

On the sum of Gamma-Gamma variates with application to the fast outage probability evaluation over fading channels

“…of the order of 10 −9 ), for which the MC method is inaccurate if the sample size is not large enough [16].…”