Posterior contraction rates for non-parametric state and drift estimation
Statistics Theory
2020-08-18 v2 Statistics Theory
Abstract
We consider a combined state and drift estimation problem for the linear stochastic heat equation. The infinite-dimensional Bayesian inference problem is formulated in terms of the Kalman-Bucy filter over an extended state space, and its long-time asymptotic properties are studied. Asymptotic posterior contraction rates in the unknown drift function are the main contribution of this paper. Such rates have been studied before for stationary non-parametric Bayesian inverse problems, and here we demonstrate the consistency of our time-dependent formulation with these previous results building upon scale separation and a slow manifold approximation.
Cite
@article{arxiv.2003.09219,
title = {Posterior contraction rates for non-parametric state and drift estimation},
author = {Sebastian Reich and Paul Rozdeba},
journal= {arXiv preprint arXiv:2003.09219},
year = {2020}
}