Quantization-Based Latin Hypercube Sampling for Dependent Inputs With an Application to Sensitivity Analysis of Environmental Models

Abstract

Numerical models are essential for comprehending intricate physical phenomena in different domains. To handle their complexity, sensitivity analysis, particularly screening is crucial for identifying influential input parameters. Kernel-based methods, such as the Hilbert-Schmidt Independence Criterion (HSIC), are valuable for analyzing dependencies between inputs and outputs. Implementing HSIC requires data from the original model, which leads to the need of efficient sampling strategies to limit the number of costly numerical simulations. While, for independent input variables, existing sampling methods like Latin Hypercube Sampling (LHS) are effective in estimating HSIC with reduced variance, incorporating dependence is challenging. This article introduces a novel LHS variant, quantization-based LHS (QLHS), which leverages Voronoi vector quantization to address dependent inputs. The method provides good coverage of the range of variations in the input variables. The article outlines expectation estimators based on QLHS in various dependency settings, demonstrating their unbiasedness. The method is applied to several models of growing complexities, first on simple examples to illustrate the theory, then on more complex environmental hydrological models, when the dependence is known or not, and with more and more interactive processes and factors. The last application is on the digital twin of a French vineyard catchment (Beaujolais region) to design a vegetative filter strip and reduce water, sediment, and pesticide transfers from the fields to the river. QLHS is used to compute HSIC measures and independence tests, demonstrating its usefulness, especially in the context of complex models.