Anomaly Detection in Random Heterogeneous Media

Simón, Martín

doi:10.1007/978-3-658-10993-6

Cited by 18 publications

(1 citation statement)

References 116 publications

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“…We used the multilevel simulation technique for SDEs introduced by Giles, cf [16], with path simulation based on the Milstein scheme, cf [27], which yields a fast and scalable massively parallel Monte Carlo sampling algorithm. For the sake of brevity we refer to the PhD thesis [40] of the author for further details. See also the related recent work by Gloria and Mourrat [17], where numerical homogenization based on random walks in random environments for discrete difference equations is studied.…”

Section: Precomputationsmentioning

confidence: 99%

Bayesian anomaly detection in heterogeneous media with applications to geophysical tomography

Simón

2014

Inverse Problems

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In this paper, we consider the problem of detecting a parameterized anomaly in an isotropic, stationary and ergodic conductivity random field via electrical impedance tomography. A homogenization result for a stochastic forward problem built on the complete electrode model is derived, which serves as the basis for a two-stage numerical method in the framework of Bayesian inverse problems. The novelty of this method lies in the introduction of an enhanced error model accounting for the approximation errors that result from reducing the full forward model to a homogenized one. In the first stage, a MAP estimate for the reduced forward model equipped with the enhanced error model is computed. Then, in the second stage, a bootstrap prior based on the first stage results is defined and the resulting posterior distribution is sampled via Markov chain Monte Carlo. We provide the theoretical foundation of the proposed method, discuss different aspects of a numerical implementation and present numerical experiments to support our findings.

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