Kolyan Ray (Imperial College London)

Bayesian nonparametric inference in a McKean-Vlasov model

Abstract: We study nonparametric estimation of the interaction term in a McKean-Vlasov model where noisy observations are drawn from the nonlinear parabolic PDE arising in the mean-field limit as the number particles grows to infinity. In this model, the long-time invariant state can be uninformative about the interaction potential. We therefore show that under certain regularity conditions on the initial state, the short-time behaviour of this system contains sufficient information to consistently recover the interaction potential using Gaussian process priors. This involves establishing a stability-type estimate for this PDE to solve the resulting inverse problem.