{
  "id": "2003.09219",
  "version": "v1",
  "published": "2020-03-20T12:11:29.000Z",
  "updated": "2020-03-20T12:11:29.000Z",
  "title": "Posterior contraction rates for non-parametric state and drift estimation",
  "authors": [
    "Sebastian Reich",
    "Paul Rozdeba"
  ],
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-20T12:11:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62G20",
      "62G05",
      "60H15",
      "62F15",
      "62M20"
    ],
    "keywords": [
      "drift estimation",
      "non-parametric state",
      "stationary non-parametric bayesian inverse problems",
      "infinite-dimensional bayesian inference problem",
      "linear stochastic heat equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}