## Séminaire de recherche Opérations - "Random Sampling for Wind-tunnel Experiment with Thinned Determinantal Point Processes" -Matthieu Wilhelm

**We tackle the problem of estimating the aerodynamic force acting over a wing from pressure measurements obtained in a wind-tunnel experiment. The technique we propose is inspired by methods from survey sampling. We suggest to use a carefully chosen random design for selecting the locations of the pressure measurements. To this aim, we leverage computer fluid dynamics (CFD) simulations to design a sampling process that aims at dramatically decreasing the uncertainty while preserving important properties like unbiasedness, controlled variance and principled quantification of the uncertainty.
Our contributions is twofold. First, we introduce a new class of non-independently thinned Determinantal Point Processes (DPP) on a manifold. Second, we use a difference estimator that, combined with the results of the CFD simulation allows one to get an accurate estimator of the force acting on the wing. The estimator has some interesting properties like unbiasedness, controlled variance and principled quantification of the uncertainty.
We also prove results about the optimal intensity of the sampling process and apply them in the context of the design of wind-tunnel experiment of a Onera M6 wing, a well-known benchmark wing in aerodynamics studies.
We consider stationary regularly varying time series. First, we review classical methods to address the time dependences of extremes based on the identification of short periods with consecutive exceedances of a high level. In this case, the extremal index gives a summary of the clustering effect. Second, we generalize this notion considering short periods, or blocks, with lp−norm above a high threshold and derive large deviation principles of blocks. Our main goal is to promote the choice p < ∞, rather than the classical one for p = ∞, where the bias is more difficult to control. We show the theory developed can be used to improve inference of functionals acting on extreme blocks. For example, the extremal index has an interpretation in this way. It can also be applied to compute accurate confidence intervals of extreme return levels.
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