Interactions between real-life problems and mathematics are useful both for practical solutions and theoretical developments. Indeed, case studies often bring original questions, that can lead to new contributions in – or at the interplay between – well-known branchs of mathematics. Below some illustrations.
I have participated to several research projects guided by applications, such the Consortium CIROQUO, the Chair OQUAIDO (leader), the ReDICE and DICE consortiums, as well as PhD thesis funded by partners from industry or technological research (Ansys, BRGM, CCR, STMicroelectronics).
I have been contributing to foster interactions between the French statistical society (SFdS) and the European network for business and industry (ENBIS), and I am regularly organizing special sessions in their annual conferences.
Customizing kernels in random field models
Motivated by a question from STMicroelectronics, the “polar” Gaussian processes defined on the unit disk, account for prior knowledge in manufacturing corresponding to radial or angular spatial correlations, and can improve spatial prediction accuracy. [More: publication, slide show]
Low-cost screening and Poincaré inequalities
Detecting unessential input variables of a computer code can be connected to Poincaré functional inequalities, giving upper bounds on Sobol sensitivity indices. Theoretical developments on Poincaré inequalities have been done on general 1-dimensional probability distributions. They resulted in 6 times sharper upper bounds in a motivating flooding application from EDF. [More: publication, slide show]
Olivier Roustant 