Repository: Freie Universit├Ąt Berlin, Math Department

Binned Multilevel Monte Carlo for Bayesian Inverse Problems with Large Data

Gantner, Robert N. and Schillings, Claudia and Schwab, Christoph (2016) Binned Multilevel Monte Carlo for Bayesian Inverse Problems with Large Data. In: Domain Decomposition Methods in Science and Engineering XXII. Springer, pp. 511-519. ISBN 978-3-319-18826-3

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Official URL: https://doi.org/10.1007/978-3-319-18827-0

Abstract

We consider Bayesian inversion of parametric operator equations for the case of a large number of measurements. Increased computational efficiency over standard averaging approaches, per measurement, is obtained by binning the data and applying a multilevel Monte Carlo method, specifying optimal forward solution tolerances per level. Based on recent bounds of convergence rates of adaptive Smolyak quadratures in Bayesian inversion for single observation data, the bin sizes in large sets of measured data are optimized and a rate of convergence of the error vs. work is derived analytically and confirmed by numerical experiments.

Item Type:Book Section
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:3000
Deposited By: Ulrike Eickers
Deposited On:06 Jun 2023 16:00
Last Modified:06 Jun 2023 16:00

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