The Annals of Applied Probability

Robust adaptive importance sampling for normal random vectors

Benjamin Jourdain and Jérôme Lelong

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Abstract

Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of importance sampling for normal random vectors. Unlike stochastic approximation, which requires very fine tuning in practice, we propose to use sample average approximation and deterministic optimization techniques to devise a robust and fully automatic variance reduction methodology. The same samples are used in the sample optimization of the importance sampling parameter and in the Monte Carlo computation of the expectation of interest with the optimal measure computed in the previous step. We prove that this highly dependent Monte Carlo estimator is convergent and satisfies a central limit theorem with the optimal limiting variance. Numerical experiments confirm the performance of this estimator: in comparison with the crude Monte Carlo method, the computation time needed to achieve a given precision is divided by a factor between 3 and 15.

Article information

Source
Ann. Appl. Probab., Volume 19, Number 5 (2009), 1687-1718.

Dates
First available in Project Euclid: 16 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1255699541

Digital Object Identifier
doi:10.1214/09-AAP595

Mathematical Reviews number (MathSciNet)
MR2569805

Zentralblatt MATH identifier
1202.62106

Subjects
Primary: 60F05: Central limit and other weak theorems 62L20: Stochastic approximation 65C05: Monte Carlo methods 90C15: Stochastic programming

Keywords
Adaptive importance sampling central limit theorem sample averaging

Citation

Jourdain, Benjamin; Lelong, Jérôme. Robust adaptive importance sampling for normal random vectors. Ann. Appl. Probab. 19 (2009), no. 5, 1687--1718. doi:10.1214/09-AAP595. https://projecteuclid.org/euclid.aoap/1255699541


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