# Metamodel construction for sensitivity analysis

## TL;DR

This paper introduces a new method for constructing a metamodel to perform sensitivity analysis on complex models using Gaussian regression, combining sparse estimation and functional ANOVA decomposition.

## Contribution

It develops a novel approach that estimates both the metamodel and sensitivity indices within a Gaussian regression framework, incorporating penalized least-squares for variable selection.

## Key findings

- The method accurately estimates sensitivity indices in simulations.
- The approach provides theoretical guarantees via an oracle inequality.
- Simulation results demonstrate effective variable subset selection.

## Abstract

We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse non-parametric estimation in multivariate Gaussian regression model. It rests on the construction of a metamodel for aproximating the Hoeffding-Sobol decomposition of m. This metamodel belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to a functional ANOVA decomposition. The estimation of the metamodel is carried out via a penalized least-squares minimization allowing to select the subsets of variables that contribute to predict the output. It allows to estimate the sensitivity indices of m. We establish an oracle-type inequality for the risk of the estimator, describe the procedure for estimating the metamodel and the sensitivity indices, and assess the performances of the procedure via a simulation study.