Discrete non-parametric kernel estimation for global sensitivity analysis

• We study a discrete kernel estimation for sensitivity analysis of a model.
• A discrete kernel estimator of ANOVA decomposition of the model is presented.
• Sensitivity indices are calculated for discrete input parameters.
• An estimator of sensitivity indices is also presented with its convergence rate.
• An application is realized for improving the reliability of environmental models.

This work investigates the discrete kernel approach for evaluating the contribution of the variance of discrete input variables to the variance of model output, via analysis of variance (ANOVA) decomposition. Until recently only the continuous kernel approach has been applied as a metamodeling approach within sensitivity analysis framework, for both discrete and continuous input variables. Now the discrete kernel estimation is known to be suitable for smoothing discrete functions. We present a discrete non-parametric kernel estimator of ANOVA decomposition of a given model. An estimator of sensitivity indices is also presented with its asymtotic convergence rate. Some simulations on a test function analysis and a real case study from agricultural have shown that the discrete kernel approach outperforms the continuous kernel one for evaluating the contribution of moderate or most influential discrete parameters to the model output.