Marc Hoffmann (Univ. Paris-Dauphine), Guillaume Sagnol (TU Berlin)
14:00 Marc Hoffmann (Univ. Paris-Dauphine): Age-structured model in a large population: combining a statistical analysis and PDEs
15:00 Tea and Coffee break
15:30 Guillaume Sagnol (TU Berlin): Optimization for statistical experiments... and vice versa
Marc Hoffmann (Univ. Paris-Dauphine): Age-structured model in a large population: combining a statistical analysis and PDEs
Motivated by improving mortality tables from human demography databases, we investigate statistical inference of a stochastic age-evolving density of a population alimented by time inhomogeneous mortality and fertility. Asymptotics are taken as the size of the population grows within a limited time horizon in which case the the observation gets closer to the solution of a PDE. The difficulty lies in controlling the stochastic approximation to the limiting PDE in a suitable sense. In this setting, we prove useful new concentration inequalities and derive oracle inequalities, the latter relating the performance of a real estimator with that of an ideal estimator which relies on perfect information supplied by an oracle, and which is not available in practice.
This is a joint work with A. Boumezoued and P. Jeunesse.
Guillaume Sagnol (TU Berlin): Optimization for statistical experiments... and vice versa
Designing optimal experiments is an important field of research at the interface between (convex/discrete) optimization and statistics. The general problem is to select the optimal conditions of experimental trials before conducting the actual experiments, this leading to a variety of optimization models with a nice structure. In the first part of this talk, I will explain where these optimization models come from, and discuss the traditional algorithms that can be used to solve these problems.
In the second part, I will discuss computer experiments using an optimal design approach. Here, one typical application is black-box optimization: Consider a complicated computer code (the black-box function), which takes several inputs and requires several hours to return a single output. We want to maximize the black-box, using a limited number of function calls by means of a sequential approach. This approach requires solving large-scale optimal design problems, and I will discuss new efficient algorithms to do so.