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In this paper, we consider the non-parametric estimation of conditional moments, which is useful for applications in global sensitivity analysis (GSA) and in the more general emulation framework. The estimation is based on the state-dependent parameter (SDP) estimation approach and allows for the estimation of conditional moments of order larger than unity. This allows one to identify a wider spectrum of parameter sensitivities with respect to the variance-based main effects, like shifts in the variance, skewness or kurtosis of the model output, so adding valuable information for the analyst, at a small computational cost.

In this paper we propose a general framework to deal with model approximation and analysis. We present a unified procedure which exploits sampling, screening and model approximation techniques in order to optimally fulfill basic requirements in terms of general applicability and flexibility, efficiency of estimation and simplicity of implementation. The sampling procedure applies Sobol' quasi-Monte Carlo sequences, which display optimal characteristics when linked to a screening procedure, such as the elementary effect test. The latter method is used to reduce the dimensionality of the problem and allows for a preliminary sorting of the factors in terms of their relative importance. Then we apply State Dependent Parameter (SDP) modelling (a model estimation approach, based on recursive filtering and smoothing estimation) to build an approximation of the computational model under analysis and to estimate the variance based sensitivity indices. The method is conceptually simple and very efficient, leading to a significant reduction in the cost of the analysis. All measures of interest are computed using a single set of quasi-Monte Carlo runs. The approach is flexible because, in principle, it can be applied with any available type of Monte Carlo sample.