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arXiv · 2003.09219

Posterior contraction rates for non-parametric state and drift estimation

Sebastian Reich·Paul Rozdeba
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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.

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Sebastian Reich, Paul Rozdeba. 2020-03-20. Posterior contraction rates for non-parametric state and drift estimation. https://arxiv.org/abs/2003.09219

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