Controlled stratification for quantile estimation

TL;DR

This paper introduces variance reduction techniques for quantile estimation in complex models using reduced models as control variates, stratification, or importance sampling, with analysis and real-world application.

Contribution

It proposes an adaptive controlled stratification method leveraging reduced models for efficient quantile estimation, improving variance reduction strategies.

Findings

Asymptotic variances demonstrate the benefits of the proposed method.

The adaptive stratification method outperforms traditional techniques.

Application to nuclear safety demonstrates practical effectiveness.

Abstract

In this paper we propose and discuss variance reduction techniques for the estimation of quantiles of the output of a complex model with random input parameters. These techniques are based on the use of a reduced model, such as a metamodel or a response surface. The reduced model can be used as a control variate; or a rejection method can be implemented to sample the realizations of the input parameters in prescribed relevant strata; or the reduced model can be used to determine a good biased distribution of the input parameters for the implementation of an importance sampling strategy. The different strategies are analyzed and the asymptotic variances are computed, which shows the benefit of an adaptive controlled stratification method. This method is finally applied to a real example (computation of the peak cladding temperature during a large-break loss of coolant accident in a nuclear reactor).