Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions
Ice-sheet models can be used to forecast ice losses from Antarctica and Greenland, but to fully quantify the risks associated with sea-level rise, probabilistic forecasts are needed. These require estimates of the probability density function (PDF) for various model parameters (e.g. the basal drag c...
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International Glaciological Society
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Online Access: | http://nora.nerc.ac.uk/id/eprint/512014/ https://nora.nerc.ac.uk/id/eprint/512014/1/s11.pdf https://doi.org/10.3189/2015JoG15J050 |
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ftnerc:oai:nora.nerc.ac.uk:512014 2023-05-15T13:49:32+02:00 Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions Arthern, Robert J. 2015-10 text http://nora.nerc.ac.uk/id/eprint/512014/ https://nora.nerc.ac.uk/id/eprint/512014/1/s11.pdf https://doi.org/10.3189/2015JoG15J050 en eng International Glaciological Society https://nora.nerc.ac.uk/id/eprint/512014/1/s11.pdf Arthern, Robert J. orcid:0000-0002-3762-8219 . 2015 Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions. Journal of Glaciology, 61 (229). 947-962. https://doi.org/10.3189/2015JoG15J050 <https://doi.org/10.3189/2015JoG15J050> Publication - Article PeerReviewed 2015 ftnerc https://doi.org/10.3189/2015JoG15J050 2023-02-04T19:42:16Z Ice-sheet models can be used to forecast ice losses from Antarctica and Greenland, but to fully quantify the risks associated with sea-level rise, probabilistic forecasts are needed. These require estimates of the probability density function (PDF) for various model parameters (e.g. the basal drag coefficient and ice viscosity). To infer such parameters from satellite observations it is common to use inverse methods. Two related approaches are in use: (1) minimization of a cost function that describes the misfit to the observations, often accompanied by explicit or implicit regularization, or (2) use of Bayes’ theorem to update prior assumptions about the probability of parameters. Both approaches have much in common and questions of regularization often map onto implicit choices of prior probabilities that are made explicit in the Bayesian framework. In both approaches questions can arise that seem to demand subjective input. One way to specify prior PDFs more objectively is by deriving transformation group priors that are invariant to symmetries of the problem, and then maximizing relative entropy, subject to any additional constraints. Here we investigate the application of these methods to the derivation of priors for a Bayesian approach to an idealized glaciological inverse problem. Article in Journal/Newspaper Antarc* Antarctica Greenland Ice Sheet Journal of Glaciology Natural Environment Research Council: NERC Open Research Archive Greenland Journal of Glaciology 61 229 947 962 |
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Open Polar |
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Natural Environment Research Council: NERC Open Research Archive |
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ftnerc |
language |
English |
description |
Ice-sheet models can be used to forecast ice losses from Antarctica and Greenland, but to fully quantify the risks associated with sea-level rise, probabilistic forecasts are needed. These require estimates of the probability density function (PDF) for various model parameters (e.g. the basal drag coefficient and ice viscosity). To infer such parameters from satellite observations it is common to use inverse methods. Two related approaches are in use: (1) minimization of a cost function that describes the misfit to the observations, often accompanied by explicit or implicit regularization, or (2) use of Bayes’ theorem to update prior assumptions about the probability of parameters. Both approaches have much in common and questions of regularization often map onto implicit choices of prior probabilities that are made explicit in the Bayesian framework. In both approaches questions can arise that seem to demand subjective input. One way to specify prior PDFs more objectively is by deriving transformation group priors that are invariant to symmetries of the problem, and then maximizing relative entropy, subject to any additional constraints. Here we investigate the application of these methods to the derivation of priors for a Bayesian approach to an idealized glaciological inverse problem. |
format |
Article in Journal/Newspaper |
author |
Arthern, Robert J. |
spellingShingle |
Arthern, Robert J. Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions |
author_facet |
Arthern, Robert J. |
author_sort |
Arthern, Robert J. |
title |
Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions |
title_short |
Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions |
title_full |
Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions |
title_fullStr |
Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions |
title_full_unstemmed |
Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions |
title_sort |
exploring the use of transformation group priors and the method of maximum relative entropy for bayesian glaciological inversions |
publisher |
International Glaciological Society |
publishDate |
2015 |
url |
http://nora.nerc.ac.uk/id/eprint/512014/ https://nora.nerc.ac.uk/id/eprint/512014/1/s11.pdf https://doi.org/10.3189/2015JoG15J050 |
geographic |
Greenland |
geographic_facet |
Greenland |
genre |
Antarc* Antarctica Greenland Ice Sheet Journal of Glaciology |
genre_facet |
Antarc* Antarctica Greenland Ice Sheet Journal of Glaciology |
op_relation |
https://nora.nerc.ac.uk/id/eprint/512014/1/s11.pdf Arthern, Robert J. orcid:0000-0002-3762-8219 . 2015 Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions. Journal of Glaciology, 61 (229). 947-962. https://doi.org/10.3189/2015JoG15J050 <https://doi.org/10.3189/2015JoG15J050> |
op_doi |
https://doi.org/10.3189/2015JoG15J050 |
container_title |
Journal of Glaciology |
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61 |
container_issue |
229 |
container_start_page |
947 |
op_container_end_page |
962 |
_version_ |
1766251511018422272 |