Repository: Freie Universität Berlin, Math Department

Multilevel Monte Carlo for Bayesian Inverse Problems

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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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)
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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