Unbiasedness of some generalized adaptive multilevel splitting algorithms

Charles-Edouard Bréhier (1, 2) , Maxime Gazeau (3) , Ludovic Goudenège (4) , Tony Lelièvre (5, 6) , Mathias Rousset (5, 6)

1 ICJ - Institut Camille Jordan
2 PSPM - Probabilités, statistique, physique mathématique
3 LISA (UMR_7583) - Laboratoire Interuniversitaire des Systèmes Atmosphériques
4 FR3487 - Fédération de Mathématiques de l'Ecole Centrale Paris
5 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
6 MATHERIALS - MATHematics for MatERIALS

We introduce a generalization of the Adaptive Multilevel Splitting algorithm in the discrete time dynamic setting, namely when it is applied to sample rare events associated with paths of Markov chains. By interpreting the algorithm as a sequential sampler in path space, we are able to build an estimator of the rare event probability (and of any non-normalized quantity associated with this event) which is unbiased, whatever the choice of the importance function and the number of replicas. This has practical consequences on the use of this algorithm, which are illustrated through various numerical experiments.

Mots clés: unbiased estimator; Rare event; Adaptive Multilevel Splitting

Domaines: Probabilités [math.PR]; Calcul [stat.CO]

Charles-Edouard Bréhier, Maxime Gazeau, Ludovic Goudenège, Tony Lelièvre, Mathias Rousset. Unbiasedness of some generalized adaptive multilevel splitting algorithms. The Annals of Applied Probability, 2016, 26 (6), pp.3559 - 3601. ⟨10.1214/16-AAP1185⟩. ⟨hal-01142704⟩