4 papers · 1 filter
Data assimilation with the 2D Navier-Stokes equations: Optimal Gaussian asymptotics for the posterior measure
Dimitri Konen, Richard Nickl
A functional Bernstein - von Mises theorem is proved for posterior measures arising in a data assimilation problem with the two-dimensional Navier-Stokes equation where a Gaussian…
Bernstein-von Mises theorems for time evolution equations
Richard Nickl
We consider a class of infinite-dimensional dynamical systems driven by non-linear parabolic partial differential equations with initial condition modelled by a Gaussian proce…
Bayesian Nonparametric Inference in McKean-Vlasov models
Richard Nickl, Grigorios A. Pavliotis, Kolyan Ray
We consider nonparametric statistical inference on a periodic interaction potential from noisy discrete space-time measurements of solutions of the nonlinear McKean-V…
On posterior consistency of data assimilation with Gaussian process priors: the 2D Navier-Stokes equations
Richard Nickl, Edriss S. Titi
We consider a non-linear Bayesian data assimilation model for the periodic two-dimensional Navier-Stokes equations with initial condition modelled by a Gaussian process prior. We s…