Cai, X;
McEwen, JD;
Pereyra, M;
(2022)
Proximal nested sampling for high-dimensional Bayesian model selection.
Statistics and Computing
, 32
(5)
, Article 87. 10.1007/s11222-022-10152-9.
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Abstract
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal likelihood (model evidence), which is computationally challenging, prohibiting its use in many high-dimensional Bayesian inverse problems. With Bayesian imaging applications in mind, in this work we present the proximal nested sampling methodology to objectively compare alternative Bayesian imaging models for applications that use images to inform decisions under uncertainty. The methodology is based on nested sampling, a Monte Carlo approach specialised for model comparison, and exploits proximal Markov chain Monte Carlo techniques to scale efficiently to large problems and to tackle models that are log-concave and not necessarily smooth (e.g., involving ℓ1 or total-variation priors). The proposed approach can be applied computationally to problems of dimension O(10 6) and beyond, making it suitable for high-dimensional inverse imaging problems. It is validated on large Gaussian models, for which the likelihood is available analytically, and subsequently illustrated on a range of imaging problems where it is used to analyse different choices of dictionary and measurement model.
| Type: | Article |
|---|---|
| Title: | Proximal nested sampling for high-dimensional Bayesian model selection |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11222-022-10152-9 |
| Publisher version: | https://doi.org/10.1007/s11222-022-10152-9 |
| Language: | English |
| Additional information: | Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Nested sampling MCMC sampling, Marginal likelihood, Bayesian evidence, Inverse problems, Proximal optimisation, Model selection |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Space and Climate Physics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10164212 |
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