Emulation of Stochastic Simulators Using Generalized Lambda Models

Abstract

Computer simulations are used in virtually all fields of applied science and engineering to predict the behaviour of complex systems. In the context of uncertainty quantification and optimization, a large number of simulations are usually necessary, which may become intractable for high-fidelity numerical models. This problem is even more severe when it comes to stochastic simulators, which do not provide a deterministic outcome for a given set of input parameters, but rather a realization of a random variable. In a recent paper, we developed a novel surrogate model for stochastic simulators. In that framework, the response distribution is assumed to be a generalized lambda distribution. The associated distribution parameters are cast as functions of input variables and represented by polynomial chaos expansions. In this paper, we propose a new fitting procedure to construct such a surrogate model, which combines the maximum conditional likelihood estimation with (modified) feasible generalized least-squares. This method does not require repeated model evaluations for the same input parameters, so it is more versatile than the existing replication-based approaches. We compare the new method with the state-of-the-art nonparametric kernel estimator on two analytical examples and case studies. The performance of the proposed method is illustrated in terms of the accuracy of both the response distribution approximation and statistical quantities depending on the specific focus of the application.