Title: Non-parametric estimation of diffusions and Bayesian posterior contraction rates

Abstract: We consider the problem of recovering the drift and diffusion coefficients of a scalar SDE, given some observations of a sample path. In this talk I will consider the cases where the observations are either continuous, high frequency or low frequency, and give an overview of results on minimax optimal convergence rates for these cases, as the observation window goes to infinity. I'll then focus on the recent work of R. Nickl and J. Sohl, in which they show that the minimax optimal rate is attained by the posterior distribution in the low frequency non-parametric regime. I'll provide the main result and some example prior distributions, and if time permits, outline the main ideas of the proof.