A Bayesian Solution to Characterizing Uncertainty in Inverse Problems
Shuai Fu1,2, Mathieu Couplet1, Nicolas Bousquet1
1Dep. MRI (Industrial Risk Management), EDF R&D, Chatou, Ile-de-France, France; 2Dep. Mathematiques, Université Paris-Sud, Orsay, Ile-de-France, France

The problem considered here is the inference of a non-observed stochastic quantity on the basis of some noisy measurements of another observed data which can be described as a function of the former. An important particularity is that this function related to a physical model is generally quite time-consuming and for this reason a limited computing budget has to be managed. Moreover, the purpose is also to take into account of the available expert knowledge in the situation of relatively few data.

To cope with these issues, we propose a bayesian framework including a kriging version of the expensive numerical function. The statistical model studied assumes a multinormal distribution prior for the missing data as well as a multinormal-Wishart prior for the variance term. A MCMC algorithm is carried out to infer the posterior distribution of interest and results are obtained for an environmental industrial application. The question < a smart choice of the design of experiments (DOE) > is investigated, which should be realised and completed sequentially under a reasonable quality criterion, so called < adaptive kriging method >.

Keywords: Bayesian; Uncertainty; Inverse problem; Kriging

Biography: Shuai FU, who started her Ph. D research from November 2009, is advised by Gilles Celeux, within team SELECT (Model Selection and Statistical Learning), INRIA Saclay as well as department MRI (Industrial Risk Management), EDF R&D, about the subject “Inverse problem in uncertainty analysis”. Before the Ph.D research, she completed her master's study in Financial Mathematics (DEA EL Karoui) at University of Paris 6, following her dual bachelor's degrees in Applicated Mathematics at University of Lille 1 and Harbin Institute of Technology in China.