Importance Sampling for rare events and conditioned random walks

Michel Broniatowski (1) , Ya'Acov Ritov (2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 Department of Statistics

This paper introduces a new Importance Sampling scheme, called Adaptive Twisted Importance Sampling, which is adequate for the improved estimation of rare event probabilities in he range of moderate deviations pertaining to the empirical mean of real i.i.d. summands. It is based on a sharp approximation of the density of long runs extracted from a random walk conditioned on its end value.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Probabilités [math.PR]

Michel Broniatowski, Ya'Acov Ritov. Importance Sampling for rare events and conditioned random walks. 2009. ⟨hal-00422852⟩