Sampling plans for the estimation of moment-independent importance measures

AbstractThe numerical and computational aspects underlying the approximation of moment independent sensitivity measures are discussed. Sampling plans based on column substitution and column permutations are evaluated and compared for both analytical test cases and a practical application. The influence of the sampling strategy (simple random, latin hypercube or quasi-random sequences) is investigated

Variational methods

International audienceThis contribution presents derivative-based methods for local sensitivity analysis, called Variational Sensitivity Analysis (VSA). If one defines an output called the response function, its sensitivity to inputs variations around a nominal value can be studied using derivative (gradient) information. The main issue of VSA is then to provide an efficient way of computing gradients. This contribution first presents the theoretical grounds of VSA: framework and problem statement, tangent and adjoint methods. Then it covers pratical means to compute derivatives, from naive to more sophisticated approaches, discussing their various 2 merits. Finally, applications of VSA are reviewed and some examples are presented, covering various applications fields: oceanography, glaciology, meteorology

Mesh Refinement Strategies for Solving Singularly Perturbed Reaction-Diffusion Problems

We consider the numerical approximation of singularly perturbed reaction-di#usion problem over a square. Two di#erent approaches are compared namely: adaptive isotropic mesh refinement and anisotropic mesh refinement. Thus, we compare the h-refinement and the Shishkin mesh approaches numerically with PLTMG software [3]. It is shown how isotropic elements lead to over-refinement and how anisotropic mesh refinement is much more e#cient in thin boundary layers. 1 Introduction The numerical solution of singularly perturbed boundary value problems has recently received much attention. In fact, problems of this type arise in many areas, such as fluid mechanics, heat transfer as well as problems in structural mechanics posed over thin domains. The solution of singularly perturbed elliptic problem will, in general contain boundary layers along the boundary of the domain. If in addition, the domain contains corners then the solution will also include singularities in the neighborhood of each v..

Contribution to the sample mean plot for graphical and numerical sensitivity analysis

a b s t r a c t The contribution to the sample mean plot, originally proposed by Sinclair, is revived and further developed as practical tool for global sensitivity analysis. The potentials of this simple and versatile graphical tool are discussed. Beyond the qualitative assessment provided by this approach, a statistical test is proposed for sensitivity analysis. A case study that simulates the transport of radionuclides through the geosphere from an underground disposal vault containing nuclear waste is considered as a benchmark. The new approach is tested against a very efficient sensitivity analysis method based on state dependent parameter meta-modelling

Model emulation and moment-independent sensitivity analysis: An application to environmental modeling

Moment-independent sensitivity methods are attracting increasing attention among practitioners, since they provide a thorough way of investigating the sensitivity of model output under uncertainty. However, their estimation is challenging, especially in the presence of computationally intensive models. We argue that replacement of the original model by a metamodel can contribute in lowering the computation burden. A numerical estimation procedure is set forth. The procedure is first tested on analytical cases with increased structural complexity. We utilize the emulator proposed in Ratto and Pagano (2010). Results show that the emulator allows an accurate estimation of density-based sensitivity measures, when the main structural features of the original model are captured. However, performance deteriorates for a model with interactions of order higher than 2. For this test case, also a kriging emulator is investigated, but no gain in performance is registered. However, an accurate estimation is obtained by applying a logarithmic transformation of the model output for both the kriging and Ratto and Pagano (2010) emulators. These findings are then applied to the investigation of a benchmark environmental case study, the LevelE model. Results show that use of the metamodel allows an efficient estimation of moment-independent sensitivity measures while leading to a notable reduction in computational burde

Moment Independent Importance Measures: New Results and Analytical Test Cases

Moment independent methods for the sensitivity analysis of model output are attracting growing attention among both academicians and practitioners. However, the lack of benchmarks against which to compare numerical strategies forces one to rely on ad-hoc experiments in estimating the sensitivity measures. This paper introduces a methodology that allows one to obtain moment independent sensitivity measures analytically. We illustrate the procedure by implementing four test cases with different model structures and model input distributions. Numerical experiments are performed at increasing sample size to check convergence of the sensitivity estimates to the analytical values