Work

Analysis of Adaptive Multilevel Splitting algorithms in an idealized case

Year: 2014

Type: article

Abstract: The Adaptive Multilevel Splitting algorithm is a very powerful and versatile method to estimate rare events probabilities. It is an iterative procedure on an interacting particle system, where at each step, the $k$ less well-adapted particles among $n$ are killed while $k$ new better adapted particles are resampled according to a conditional law. We analyze the algorithm in the idealized setting of an exact resampling and prove that the estimator of the rare event probability is unbiased whatever $k$. We also obtain a precise asymptotic expansion for the variance of the estimator and the cost of the algorithm in the large $n$ limit, for a fixed $k$.

Source: Springer Link (Chiba Institute of Technology)

DOI: 10.48550/arxiv.1405.1352

Authors: Bréhier, Charles-Edouard, Lelievre, Tony, Rousset, Mathias

Institutions: Institut national de recherche en sciences et technologies du numérique, CERMICS

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, FP7 Ideas: European Research Council

Awards: Molecular Simulation: modeling, algorithms and mathematical analysis, G3207356259, G896728979