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MCMC for the evaluation of Gaussian approximations to Bayesian inverse problems in groundwater flow
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Iglesias, Marco, Law, K. J. H. and Stuart, A. M. (2012) MCMC for the evaluation of Gaussian approximations to Bayesian inverse problems in groundwater flow. In: NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012, Kos, Greece, 19-25 September. Published in: AIP Conference Proceedings, Vol. 1479 pp. 920-923. ISBN 978-0-7354-1091-6. doi:10.1063/1.4756292 ISSN 0094-243X.
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Official URL: http://dx.doi.org/10.1063/1.4756292
Abstract
The goal of the present work is twofold. First, we use the modified random walk Markov Chain Monte Carlo (MCMC) method introduced by [1] to sample from the posterior distribution that arises from Bayesian data assimilation in a groundwater model. Second, we use these samples to evaluate the performance of standard ad hoc Gaussian approximations of the posterior. We use a synthetic experiment to show that our MCMC implementation converges faster than the standard random walk MCMC. In addition, we design a controlled experiment to evaluate the performance of standard Gaussian approximations of the posterior. More precisely, we use our MCMC characterization of the posterior to compare the uncertainty quantification properties of the ensemble Kalman filter (EnKF), randomized maximum likelihood (RML) and maximum a posterior (MAP) methods.
| Item Type: | Conference Item (Paper) | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | AIP Conference Proceedings | ||||
| Publisher: | American Institute of Physics | ||||
| ISBN: | 978-0-7354-1091-6 | ||||
| ISSN: | 0094-243X | ||||
| Official Date: | 2012 | ||||
| Dates: |
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| Volume: | Vol. 1479 | ||||
| Page Range: | pp. 920-923 | ||||
| DOI: | 10.1063/1.4756292 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Conference Paper Type: | Paper | ||||
| Title of Event: | NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012 | ||||
| Type of Event: | Conference | ||||
| Location of Event: | Kos, Greece | ||||
| Date(s) of Event: | 19-25 September |
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