Emulation of stochastic simulators using generalized lambda models

Stochastic simulators are ubiquitous in many fields of applied sciences and engineering. In the context of uncertainty quantification and optimization, a large number of simulations is usually necessary, which becomes intractable for high-fidelity models. Thus surrogate models of stochastic simulators have been intensively investigated in the last decade. In this paper, we present a novel approach to surrogating the response distribution of a stochastic simulator which uses generalized lambda distributions, whose parameters are represented by polynomial chaos expansions of the model inputs. As opposed to most existing approaches, this new method does not require replicated runs of the simulator at each point of the experimental design. We propose a new fitting procedure which combines maximum conditional likelihood estimation with (modified) feasible generalized least-squares. We compare our method with state-of-the-art nonparametric kernel estimation on four different applications stemming from mathematical finance and epidemiology. Its performance is illustrated in terms of the accuracy of both the mean/variance of the stochastic simulator and the response distribution. As the proposed approach can also be used with experimental designs containing replications, we carry out a comparison on two of the examples, showing that replications do not necessarily help to get a better overall accuracy and may even worsen the results (at a fixed total number of runs of the simulator).