Sequential Monte Carlo for rare event estimation

Frédéric Cérou (1, 2) , Pierre del Moral (3) , Teddy Furon (4) , Arnaud Guyader (1, 2)

1 ASPI - Applications of interacting particle systems to statistics
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 ALEA - Advanced Learning Evolutionary Algorithms
4 TEXMEX - Multimedia content-based indexing

This paper discusses a novel strategy for simulating rare events and an associated Monte Carlo estimation of tail probabilities. Our method uses a system of interacting particles and exploits a Feynman-Kac representation of that system to analyze their fluctuations. Our precise analysis of the variance of a standard multilevel splitting algorithm reveals an opportunity for improvement. This leads to a novel method that relies on adaptive levels and produces, in the limit of an idealized version of the algorithm, estimates with optimal variance. The motivation for this theoretical work comes from problems occurring in watermarking and fin- gerprinting of digital contents, which represents a new field of applications of rare event simulation techniques. Some numerical results show performance close to the idealized version of our technique for these practical applications.

Mots clés: Rare event; Sequential importance sampling; Feynman-Kac formula; Metropolis-Hastings; Fingerprinting; Watermarking

Domaines: Calcul [stat.CO]

Frédéric Cérou, Pierre del Moral, Teddy Furon, Arnaud Guyader. Sequential Monte Carlo for rare event estimation. Statistics and Computing, 2012, 22 (3), pp.795-908. ⟨10.1007/s11222-011-9231-6⟩. ⟨inria-00584352⟩