Simulation and estimation of extreme quantiles and extreme probabilities

Arnaud Guyader (1, 2) , Nicolas W. Hengartner (3) , Eric Matzner-Løber (2)

1 ASPI - Applications of interacting particle systems to statistics
2 MASS - Département Mathématiques appliquées et sciences sociales - Rennes 2
3 LANL - Los Alamos National Laboratory

Let X be a random vector with distribution μ on ℝ^d and Φ be a mapping from ℝ^d d to ℝ. That mapping acts as a black box, e.g., the result from some computer experiments for which no analytical expression is available. This paper presents an efficient algorithm to estimate a tail probability given a quantile or a quantile given a tail probability. The algorithm improves upon existing multilevel splitting methods and can be analyzed using Poisson process tools that lead to exact description of the distribution of the estimated probabilities and quantiles. The performance of the algorithm is demonstrated in a problem related to digital watermarking.

Domaines: Probabilités [math.PR]

Arnaud Guyader, Nicolas W. Hengartner, Eric Matzner-Løber. Simulation and estimation of extreme quantiles and extreme probabilities. Applied Mathematics and Optimization, 2011, 64 (2), pp.171-196. ⟨10.1007/s00245-011-9135-z⟩. ⟨hal-00911891⟩