Dear Colleagues, we would like to invite you to the following seminar by Langxuan Su (Duke University) to be held next Wednesday in Pisa and online via Google Meets. The organizers, A. Agazzi and F. Grotto
------------------------------------------------------- Location: Sala Seminari, Dipartimento di Matematica, Pisa
Google Meet Link: https://meet.google.com/gji-phwo-vbg
Time: March 23, 2022, 15:00 CET
Speaker: Langxuan Su (Duke University)
Title: A Large Deviation Approach to Posterior Consistency in Dynamical Systems
Abstract: We provide asymptotic results concerning (generalized) Bayesian inference for certain dynamical systems based on a large deviation approach. Given a sequence of observations, a class of parametrized model processes and a loss function, we specify the generalized posterior distribution. We state conditions on the model family and the loss function such that the posterior distribution converges. The two conditions we require are: (1) a conditional large deviation behavior for a single model process, and (2) an exponential continuity condition over the model family for the map from the parameter to the loss incurred between a model process and the observations. The proposed framework is quite general, we apply it to two very different classes of dynamical systems: continuous time hypermixing processes and Gibbs processes on shifts of finite type. We also show that the generalized posterior distribution concentrates asymptotically on those parameters that minimize the expected loss and a divergence term, hence proving posterior consistency.