Le Bail, M Mathis (2022) Estimation of the probability of the union of rare events PRE - Research Project, ENSTA.



We consider the estimation of the probability µ of a union of J rare events Hj defined by a random variable X. To do this, we compare the ALOE estimator and the directional estimator from the papers [AC18] and [AK18] published the same year and which use two different approaches. The ALOE estimator is retained because of its better efficiency and its ability to be generalized to a large number of distributions. The latter, in the paper [AC18], is indeed only implemented for Gaussian distributions and rare events whose boundary is defined by a line. We modify this estimator using an adaptive multilevel splitting method to generalise it to a larger number of distributions and for rare events whose boundaries are defined more generally by the equation h(x) = τ where h : R d → R is a general function that we assume we can evaluate at any point x ∈ R d.This new estimator is compared to direct estimation of µ using the multilevel splitting method through a theoretical study and two numerical examples

Item Type:Thesis (PRE - Research Project)
Uncontrolled Keywords:Rare events, Monte Carlo method, Importance sampling, Markov Chain Monte Carlo
Subjects:Mathematics and Applications
ID Code:9433
Deposited By:M. bibnum1 bibnum1
Deposited On:07 juin 2023 12:10
Dernière modification:07 juin 2023 12:10

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