******************************************************************* STATISTICS SEMINARS @ COLLEGIO CARLO ALBERTO *******************************************************************

Venerdi 6 Maggio 2016 alle ore 16:00, presso l’Aula Rossa del Collegio Carlo Alberto, Moncalieri (TO), si terra' il seguente seminario:

Richard NICKL (University of Cambridge)

NONPARAMETRIC BAYESIAN INFERENCE FOR DISCRETELY SAMPLED DIFFUSIONS

We consider the nonlinear statistical inverse problem of making inference on the unknown parameters of a diffusion process describing the solution of a stochastic differential equation. The observation regime is such that the process is sampled at discrete time points that are a fixed distance apart, and we investigate the asymptotic regime when more samples accrue in the time horizon (thus avoiding unrealistic `high frequency’ assumptions). We shall briefly review frequentist estimation techniques and then turn to Bayesian nonparametric approaches to the problem, which have recently been shown to be computationally tractable (work of A. Stuart, G. Roberts and co-authors). A theory of frequentist contraction rates for the posterior distribution has been elusive for several years, and we present first rigorous, minimax optimal contraction rates for posterior distributions arising from natural prior distributions on infinite-dimensional parameter spaces on the drift and diffusion coefficient. We will discuss what can be learnt from these results for the choice of prior in such problems, as well as for the Bayesian analysis of general nonlinear inverse problems. In the proofs we obtain some new (functional) concentration inequalities for additive functionals of Markov chains arising from diffusions that are of independent interest. This is joint work with Jakob Soehl (Cambridge), see http://arxiv.org/abs/1510.05526

Tutti gli interessati sono invitati a partecipare.

Il seminario e' organizzato dalla "de Castro" Statistics Initiative (http://www.carloalberto.org/stats) in collaborazione con il Collegio Carlo Alberto.

Cordiali saluti, Matteo Ruggiero

--- Matteo Ruggiero University of Torino and Collegio Carlo Alberto www.matteoruggiero.it