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Hyperpriors for Matérn fields with applications in Bayesian inversion

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Title: Hyperpriors for Matérn fields with applications in Bayesian inversion
Authors: Roininen, L
Girolami, M
Lasanen, S
Markkanen, M
Item Type: Journal Article
Abstract: We introduce non-stationary Matérn field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors. We model both the hyperprior and the Matérn prior as continuous-parameter random fields. As hypermodels, we use Cauchy and Gaussian random fields, which we map suitably to a desired correlation length-scaling range. For computations, we discretise the models with finite difference methods. We consider the convergence of the discretised prior and posterior to the discretisation limit. We apply the developed methodology to certain interpolation, numerical differentiation and deconvolution problems, and show numerically that we can make Bayesian inversion which promotes competing constraints of smoothness and edge-preservation. For computing the conditional mean estimator of the posterior distribution, we use a combination of Gibbs and Metropolis-within-Gibbs sampling algorithms.
Issue Date: 1-Feb-2019
Date of Acceptance: 31-Jan-2019
URI: http://hdl.handle.net/10044/1/66155
DOI: https://dx.doi.org/10.3934/ipi.2019001
ISSN: 1930-8345
Publisher: American Institute of Mathematical Sciences
Start Page: 1
End Page: 29
Journal / Book Title: Inverse Problems and Imaging
Volume: 13
Issue: 1
Copyright Statement: © 2019 American Institute of Mathematical Sciences. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Inverse Problems and Imaging following peer review. The definitive publisher-authenticated version, February 2019, 13(1): 1-29 is available online at: https://dx.doi.org/10.3934/ipi.2019001.
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/K034154/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Physics, Mathematical
Mathematics
Physics
Bayesian statistical estimation
inverse problems
Matern fields
hypermodels
convergence
FRAMEWORK
PRIORS
math.ST
stat.TH
Publication Status: Published
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences