Global sensitivity analysis of rare event probabilities

TL;DR

This paper introduces a computationally efficient method combining subset simulation and polynomial chaos expansion to analyze the sensitivity of rare event probabilities to model hyper-parameters, demonstrated on practical and analytical examples.

Contribution

It presents a novel double-loop sampling approach that accelerates and approximates the sensitivity analysis of rare event probabilities, improving efficiency and applicability.

Findings

Method is computationally efficient and simple to implement.

Performance demonstrated on subsurface flow and analytical example.

Enables sensitivity analysis of rare events with fewer computations.

Abstract

By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the model parameters. Hence, understanding the sensitivity of the computed rare event probabilities to the hyper-parameters that define the distribution law of the model parameters is crucial. We show that by (i) accelerating the calculation of rare event probabilities through subset simulation and (ii) approximating the resulting probabilities through a polynomial chaos expansion, the global sensitivity of such problems can be analyzed through a double-loop sampling approach. The resulting method is conceptually simple and computationally efficient; its performance is illustrated on a subsurface flow application and on an analytical example.