Gantner, Robert N. and Schillings, Claudia and Schwab, Christoph
(2014)
*Multilevel Monte Carlo for Bayesian Inverse Problems.*
In: Swiss Numerics Day 2014, April 2014, Universität Zürich.

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## Abstract

Introduction In recent years, various methods have been developed for solving parametric operator equations, focusing on the estimation of parameters given measurements of the parametric solution, subject to a stochastic observation error model. The Bayesian approach [7] to such inverse problems for PDEs will be considered here and solved using adaptive, deterministic sparse tensor Smolyak quadrature schemes from [4, 5]. Multiple solutions of the Bayesian inverse problem based on different measurements are often averaged using a standard Monte Carlo approach. We develop a multilevel Monte Carlo method achieving an error of the same order while requiring less work [1, 2, 3].

Item Type: | Conference or Workshop Item (Paper) |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group |

ID Code: | 3007 |

Deposited By: | Ulrike Eickers |

Deposited On: | 12 Jun 2023 14:55 |

Last Modified: | 12 Jun 2023 14:55 |

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