Sequential inverse problems Bayesian principles and the logistic map example
Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimens...
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| Format: | Conference item |
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2010
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| _version_ | 1797083106575908864 |
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| author | Duan, L Farmer, C Moroz, I |
| author_facet | Duan, L Farmer, C Moroz, I |
| author_sort | Duan, L |
| collection | OXFORD |
| description | Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection. |
| first_indexed | 2024-03-07T01:37:13Z |
| format | Conference item |
| id | oxford-uuid:959f1092-c2d0-48ab-a3dd-8c4db0d8828d |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:37:13Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:959f1092-c2d0-48ab-a3dd-8c4db0d8828d2022-03-26T23:47:19ZSequential inverse problems Bayesian principles and the logistic map exampleConference itemhttp://purl.org/coar/resource_type/c_5794uuid:959f1092-c2d0-48ab-a3dd-8c4db0d8828dMathematical Institute - ePrints2010Duan, LFarmer, CMoroz, IBayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection. |
| spellingShingle | Duan, L Farmer, C Moroz, I Sequential inverse problems Bayesian principles and the logistic map example |
| title | Sequential inverse problems Bayesian principles and the
logistic map example |
| title_full | Sequential inverse problems Bayesian principles and the
logistic map example |
| title_fullStr | Sequential inverse problems Bayesian principles and the
logistic map example |
| title_full_unstemmed | Sequential inverse problems Bayesian principles and the
logistic map example |
| title_short | Sequential inverse problems Bayesian principles and the
logistic map example |
| title_sort | sequential inverse problems bayesian principles and the logistic map example |
| work_keys_str_mv | AT duanl sequentialinverseproblemsbayesianprinciplesandthelogisticmapexample AT farmerc sequentialinverseproblemsbayesianprinciplesandthelogisticmapexample AT morozi sequentialinverseproblemsbayesianprinciplesandthelogisticmapexample |