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dc.contributor.authorSuuronen, Jarkko
dc.contributor.authorRoininen, Lassi
dc.contributor.authorK. Chada, Neil
dc.date.accessioned2022-04-20T10:28:51Z
dc.date.available2021-06-02T07:35:59Z
dc.date.available2022-04-20T10:28:51Z
dc.date.issued2022-03-25
dc.identifier.citationSuuronen, J., Chada, N. K., & Roininen, L. (2022). Cauchy Markov random field priors for Bayesian inversion. Statistics and Computing, 32(2). https://doi.org/10.1007/s11222-022-10089-z
dc.identifier.doi10.1007/s11222-022-10089-z
dc.identifier.urihttp://hdl.handle.net/10754/669335
dc.description.abstractThe use of Cauchy Markov random field priors in statistical inverse problems can potentially lead to posterior distributions which are non-Gaussian, high-dimensional, multimodal and heavy-tailed. In order to use such priors successfully, sophisticated optimization and Markov chain Monte Carlo (MCMC) methods are usually required. In this paper, our focus is largely on reviewing recently developed Cauchy difference priors, while introducing interesting new variants, whilst providing a comparison. We firstly propose a one-dimensional second order Cauchy difference prior, and construct new first and second order two-dimensional isotropic Cauchy difference priors. Another new Cauchy prior is based on the stochastic partial differential equation approach, derived from Mat\'{e}rn type Gaussian presentation. The comparison also includes Cauchy sheets. Our numerical computations are based on both maximum a posteriori and conditional mean estimation.We exploit state-of-the-art MCMC methodologies such as Metropolis-within-Gibbs, Repelling-Attracting Metropolis, and No-U-Turn sampler variant of Hamiltonian Monte Carlo. We demonstrate the models and methods constructed for one-dimensional and two-dimensional deconvolution problems. Thorough MCMC statistics are provided for all test cases, including potential scale reduction factors.
dc.description.sponsorshipThe authors thank Dr Sari Lasanen and Prof. Heikki Haario for useful discussions. JS and LR acknowledge Academy of Finland project funding (grant numbers 334816 and 336787).NKC is supported by KAUST baseline funding.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2105.12488.pdf
dc.rightsArchived with thanks to arXiv
dc.subjectCauchy priors
dc.subjectMarkov models
dc.subjectInverse problems
dc.subjectBayesian approach
dc.subjectMetropolis algorithms
dc.subjectHMC-NUTS
dc.titleCauchy Markov Random Field Priors for Bayesian Inversion
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program, King Abdullah University of Science and Technology, Thuwal, 23955, Kingdom of Saudi Arabia
dc.eprint.versionPre-print
dc.contributor.institutionSchool of Engineering Science, Lappeenranta-Lahti University of Technology, PO Box 20, 53851 Lappeenranta, Finland
dc.identifier.arxivid2105.12488
kaust.personChada, Neil Kumar
refterms.dateFOA2021-06-02T07:37:10Z
kaust.acknowledged.supportUnitKAUST baseline funding


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