rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Bayesian non-linear statistical inverse problems
  name:
    name part: Nickl, Richard
    name part: 1980-
    role:
      role term: creator
    role:
      role term: author.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: gw
    date issued: 2023
    copyright date: 2023
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xi, 159 pages : color illustrations ; 24 cm.
  abstract: Bayesian methods based on Gaussian process priors are frequently used in statistical inverse problems arising with partial differential equations (PDEs). They can be implemented by Markov chain Monte Carlo (MCMC) algorithms. The underlying statistical models are naturally high- or infinite-dimensional, and this book presents a rigorous mathematical analysis of the statistical performance, and algorithmic complexity, of such methods in a natural setting of non-linear random design regression. Due to the non-linearity present in many of these inverse problems, natural least squares functionals are non-convex and the Bayesian paradigm presents an attractive alternative to optimization-based approaches. This book develops a general theory of Bayesian inference for non-linear forward maps and rigorously considers two PDE model examples arising with Darcy's problem and a Schrödinger equation. The focus is initially on statistical consistency of Gaussian process methods and then moves on to study local fluctuations and approximations of posterior distributions by Gaussian or log-concave measures whose curvature is described by PDE mapping properties of underlying “information operators.” Applications to the algorithmic runtime of gradient-based MCMC methods are discussed, as well as computation time lower bounds for worst case performance of some algorithms.
  note: Richard Nickl.
  note: Includes bibliographical references and index.
  subject:
    topic: Inverse problems (Differential equations)
  subject:
    topic: Probabilities
  subject:
    topic: Statistics
  classification: QA378.5 .N53 2023
  classification: 515/.357
  related item:
    title info:
      title: Zurich lectures in advanced mathematics
  identifier: 3985470537
  identifier: 9783985470532
  record info:
    record content source: YDX
    record creation date: 230719
    record change date: 20250320194604.4
    record identifier: in00004762579