Schwab, Christoph and Schillings, Claudia
(2013)
*Sparse Quadrature Approach to Bayesian Inverse Problems.*
In: SIAM Conference on Computational Science and Engineering.

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## Abstract

We consider the parametric deterministic formulation of Bayesian inverse problems with distributed parameter uncertainty from infinite dimensional, separable Banach spaces X, with uniform prior probability measure on space X of all uncertainties. Under the assumption of given observation data δ subject to additive observation noise η ∼ N (0, Γ) with positive covariance Γ, an infinite-dimensional version of Bayes’ formula has been shown in [14]. For problems with uncertain, distributed parameters u ∈ X (which could be a diffusion coefficient, elastic moduli in solid mechanics, shape of the domain D of definition of the physical problem [1], kinetic parameters in stoichiometric models of reaction-systems in biological systems [4, 7], permeability in porous media or optimal control of uncertain systems [9]), we develop a practical, adaptive computational algorithm for the efficient approximation of the infinite-dimensional integrals with respect to the Bayesian posterior (conditional on given data δ) μδ which arise in Bayes’ formula in [14]

Item Type: | Conference or Workshop Item (Lecture) |
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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: | 3009 |

Deposited By: | Ulrike Eickers |

Deposited On: | 12 Jun 2023 15:15 |

Last Modified: | 12 Jun 2023 15:15 |

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