The geometry of sloppiness
The use of mathematical models in the sciences often involves the estimation of unknown parameter values from data. Sloppiness provides information about the uncertainty of this task. In this paper, we develop a precise mathematical foundation for sloppiness as initially introduced and define rigoro...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
2018
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| Online Access: | https://eprints.nottingham.ac.uk/53659/ |
| _version_ | 1848798970214612992 |
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| author | Dufresne, Emilie Harrington, Heather A. Raman, Dhruva V. |
| author_facet | Dufresne, Emilie Harrington, Heather A. Raman, Dhruva V. |
| author_sort | Dufresne, Emilie |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | The use of mathematical models in the sciences often involves the estimation of unknown parameter values from data. Sloppiness provides information about the uncertainty of this task. In this paper, we develop a precise mathematical foundation for sloppiness as initially introduced and define rigorously key concepts, such as `model manifold', in relation to concepts of structural identifiability. We redefine sloppiness conceptually as a comparison between the premetric on parameter space induced by measurement noise and a reference metric. This opens up the possibility of alternative quantification of sloppiness, beyond the standard use of the Fisher Information Matrix, which assumes that parameter space is equipped with the usual Euclidean metric and the measurement error is infinitesimal. Applications include parametric statistical models, explicit time dependent models, and ordinary differential equation models. |
| first_indexed | 2025-11-14T20:28:14Z |
| format | Article |
| id | nottingham-53659 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:28:14Z |
| publishDate | 2018 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-536592018-09-04T09:03:28Z https://eprints.nottingham.ac.uk/53659/ The geometry of sloppiness Dufresne, Emilie Harrington, Heather A. Raman, Dhruva V. The use of mathematical models in the sciences often involves the estimation of unknown parameter values from data. Sloppiness provides information about the uncertainty of this task. In this paper, we develop a precise mathematical foundation for sloppiness as initially introduced and define rigorously key concepts, such as `model manifold', in relation to concepts of structural identifiability. We redefine sloppiness conceptually as a comparison between the premetric on parameter space induced by measurement noise and a reference metric. This opens up the possibility of alternative quantification of sloppiness, beyond the standard use of the Fisher Information Matrix, which assumes that parameter space is equipped with the usual Euclidean metric and the measurement error is infinitesimal. Applications include parametric statistical models, explicit time dependent models, and ordinary differential equation models. 2018-05-31 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/53659/1/Dufresne-Raman-Harrington--GeometryOfSloppiness.pdf Dufresne, Emilie, Harrington, Heather A. and Raman, Dhruva V. (2018) The geometry of sloppiness. Journal of Algebraic Statistics . ISSN 1309-3452 (In Press) |
| spellingShingle | Dufresne, Emilie Harrington, Heather A. Raman, Dhruva V. The geometry of sloppiness |
| title | The geometry of sloppiness |
| title_full | The geometry of sloppiness |
| title_fullStr | The geometry of sloppiness |
| title_full_unstemmed | The geometry of sloppiness |
| title_short | The geometry of sloppiness |
| title_sort | geometry of sloppiness |
| url | https://eprints.nottingham.ac.uk/53659/ |