My present research focuses on small data, i.e. data which are hardly available, such as outputs of time-consuming computer codes. Such numerical codes model complex systems in various domains: natural risks (e.g. marine submersion), energy, transports, etc. My contributions are methodological and aim at answering several questions:
- How constructing faithful stochastic models (or metamodels) for small data?
- How designing experiments (initially and sequentially)?
- How quantifying the influence of inputs on the output of interest?
- How optimizing a multivariate function when only few observations are available?
Applications arouse new questions in – or at the interplay between – several fields in mathematics, and result in original contributions in random field models, design of experiments, Sobol-Hoeffding (ANOVA) decomposition, and also, more surprisingly, in functional (Poincaré) inequalities.
Olivier Roustant 