Résumé
When a model contains a large number of parameters, sensitivity analysis is often used to select the parameters to be estimated among those identified as the most influent. This selection procedure is based on simulated data and is different from the model validation procedure that is based on real data. Nevertheless, these two processes are interrelated in their objectives and it is interesting to quantify the benefit of this practice in terms of MSEP (Mean Square Error of Prediction) and MSE (Mean Square Error) criteria. In this paper, we investigate the relationship between the model validation criteria and the sensitivity indices. We first formalize the process of selecting the parameters to be estimated by sensitivity analysis and of fixing other parameters at their nominal value. Under the linear model, we show an explicit relationship between the sensitivity indices of model parameters and the model quality criteria such as MSE and MSEP. We also study the impact on prediction quality of both the design of experiments (input variables of the model) and the point where sensitivity analysis is performed. In these simulations, we compare the procedure of parameters selection by sensitivity indices and the LASSO method well suited for sparse model. The results show that estimating the most influent parameters reduces the MSE and the MSEP all things being equal. However this reduction is not systematic. Indeed, the relationship between MSEP and sensitivity indices is complex and depends heavily on experimental design. For example, only an orthogonal experimental design ensures a systematic reduction of MSEP. Moreover, the results depend on the support points of sensitivity analysis. The performance of the parameters selection by sensitivity analysis is equivalent to that of LASSO in terms of MSEP if we have relevant prior knowledge on the degree of uncertainty in different parameters to perform the sensitivity analysis. The practical implications of the results are discussed at the end of the paper.