University of Oulu

Discretisation-invariant and computationally efficient correlation priors for Bayesian inversion

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Author: Roininen, Lassi1,2
Organizations: 1University of Oulu, Faculty of Science, Department of Mathematical Sciences
2University of Oulu, Sodankylä Geophysical Observatory
Format: ebook
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1.2 MB)
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Language: English
Published: 2015
Publish Date: 2015-06-05
Thesis type: Doctoral Dissertation
Defence Note: Academic dissertation to be presented with the assent of the Doctoral Training Committee of Technology and Natural Sciences of the University of Oulu, in Polaria lecture hall of the Sodankylä Geophysical Observatory on 16 June 2015 at 12 o’clock.
Tutor: Professor Markku Lehtinen
Professor Valeri Serov
Reviewer: Professor Håvard Rue
Professor Ville Kolehmainen
Opponent: Professor Håvard Rue
Professor Jouko Lampinen
Kustos: Professor Markku Lehtinen


We are interested in studying Gaussian Markov random fields as correlation priors for Bayesian inversion. We construct the correlation priors to be discretisation-invariant, which means, loosely speaking, that the discrete priors converge to continuous priors at the discretisation limit. We construct the priors with stochastic partial differential equations, which guarantees computational efficiency via sparse matrix approximations. The stationary correlation priors have a clear statistical interpretation through the autocorrelation function.

We also consider how to make structural model of an unknown object with anisotropic and inhomogeneous Gaussian Markov random fields. Finally we consider these fields on unstructured meshes, which are needed on complex domains.

The publications in this thesis contain fundamental mathematical and computational results of correlation priors. We have considered one application in this thesis, the electrical impedance tomography. These fundamental results and application provide a platform for engineers and researchers to use correlation priors in other inverse problem applications.

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Series: Sodankylä geophysical observatory publications
ISSN: 1456-3673
ISSN-L: 1456-3673
ISBN: 978-952-62-0754-4
ISBN Print: 978-952-62-0753-7
Issue: 109
Type of Publication: G5 Doctoral dissertation (articles)
Field of Science: 111 Mathematics
112 Statistics and probability
Copyright information: © University of Oulu, 2015. This publication is copyrighted. You may download, display and print it for your own personal use. Commercial use is prohibited.