Hyperpriors for Matérn fields with applications in Bayesian inversion
File(s)
Accepted version
Author(s)
Roininen, Lassi
Girolami, Mark
Lasanen, Sari
Markkanen, Markku
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.
Date Issued
2019-02-01
Date Acceptance
2019-01-31
Citation
Inverse Problems and Imaging, 2019, 13 (1), pp.1-29
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
Engineering & Physical Science Research Council (E
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000453255700001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/K034154/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Physics, Mathematical
Mathematics
Physics
Bayesian statistical estimation
inverse problems
Matern fields
hypermodels
convergence
FRAMEWORK
PRIORS
Publication Status
Published