Versatile sequential sampling algorithm using Kernel Density Estimation

Abstract

Understanding the physical mechanisms governing scientific and engineering systems requires performing experiments. Therefore, the construction of the Design of Experiments (DoE) is paramount for the successful inference of the intrinsic behavior of such systems. There is a vast literature on one-shot designs such as low discrepancy sequences and Latin Hypercube Sampling (LHS). However, in a sensitivity analysis context, an important property is the stochasticity of the DoE which is partially addressed by these methods. This work proposes a new stochastic, iterative DoE – named KDOE – based on a modified Kernel Density Estimation (KDE). It is a two-step process: (i) candidate samples are generated using Markov Chain Monte Carlo (MCMC) based on KDE, and (ii) one of them is selected based on some metric. The performance of the method is assessed by means of the C2-discrepancy space-filling criterion. KDOE appears to be as performant as classical one-shot methods in low dimensions, while it presents increased performance for high-dimensional parameter spaces. It is a versatile method which offers an alternative to classical methods and, at the same time, is easy to implement and offers customization based on the objective of the DoE.