Evaluation of gaussian processes and other methods for non-linear regression
Evaluation of gaussian processes and other methods for non-linear regression
An efficient methodology for modeling complex computer codes with Gaussian processes
Computational Statistics & Data Analysis
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Large-scale landslide prediction is typically based on numerical modeling, with computer codes generally involving a large number of input parameters. Addressing the influence of each of them on the final result and providing a ranking procedure may be useful for risk management purposes. This can be performed by a variance-based global sensitivity analysis. Nevertheless, such an analysis requires a large number of computer code simulations, which appears impracticable for computationally demanding simulations, with computation times ranging from several hours to several days. To overcome this difficulty, we propose a ''meta-model''-based strategy consisting in replacing the complex simulator by a ''statistical approximation'' provided by a Gaussian-process (GP) model. This allows computation of sensitivity measures from a limited number of simulations. For illustrative purposes, the proposed methodology is used to rank in terms of importance the properties of the elastoplastic model describing the complex behavior of the slip surface in the La Frasse landslide (Switzerland). One limitation of the GP-based methodology is that the computation of sensitivity measures is associated with uncertainty as the simulator is approximated using a training sample of small size, i.e., a limited knowledge on the ''true'' simulator. This source of uncertainty can be taken into account by treating the GP model from a Bayesian perspective. This provides the full posterior probability distribution associated with the sensitivity measures, which can be summarized by a confidence interval to outline the regions where the GP model is ''unsure.'' We show that this methodology is able to provide useful guidelines for the practical decision-making process and suggest further site investigations.