{
  "id": "1511.00524",
  "version": "v1",
  "published": "2015-11-02T14:39:25.000Z",
  "updated": "2015-11-02T14:39:25.000Z",
  "title": "Inverse Problems in a Bayesian Setting",
  "authors": [
    "Hermann G. Matthies",
    "Elmar Zander",
    "Bojana V. Rosić",
    "Alexander Litvinenko",
    "Oliver Pajonk"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1312.5048",
  "categories": [
    "math.PR"
  ],
  "abstract": "In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-02T14:39:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse problems",
      "bayesian setting",
      "convergent monte carlo sampling",
      "approximation",
      "developed sampling-free non-linear bayesian update"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151100524M"
    }
  }
}