Towards zero variance estimators for rare event probabilities - Sorbonne Université
Article Dans Une Revue ACM Transactions on Modeling and Computer Simulation Année : 2013

Towards zero variance estimators for rare event probabilities

Résumé

Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events $E_{n}:=\left( u(X_{1})+...+u(X_{n}\right) )\in A_{n}$ where the summands are i.i.d. and $E_{n}$ is a large or moderate deviation event. The approximation of the conditional density of the vector $\left( X_{1},...,X_{k_{n}}\right) $ with respect to $E_{n}$ on long runs, when $% k_{n}/n\rightarrow1$, is handled. The maximal value of $k_{n}$ compatible with a given accuracy is discussed; simulated results are presented, which enlight the gain of the present approach over classical IS schemes. Detailed algorithms are proposed.

Domaines

Calcul [stat.CO]
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Dates et versions

hal-00613346 , version 1 (04-08-2011)
hal-00613346 , version 2 (03-02-2012)

Identifiants

  • HAL Id : hal-00613346 , version 2

Citer

Michel Broniatowski, Virgile Caron. Towards zero variance estimators for rare event probabilities. ACM Transactions on Modeling and Computer Simulation, 2013, 23 (1), pp. 7, 23. ⟨hal-00613346v2⟩
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