The Geometry of Sloppiness

Emilie Sonia Dufresne; Heather A Harrington; Dhruva V Raman

The Geometry of Sloppiness

Emilie Sonia Dufresne, Heather A Harrington, Dhruva V Raman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	30-68
Number of pages	39
Journal	Journal of Algebraic Statistics
Volume	9
Issue number	1
Publication status	Published - 27 Sept 2018

Bibliographical note

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Dufresne-Raman-Harrington--GeometryOfSloppiness
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Emilie Sonia Dufresne
- emilie.dufresneyork.acuk
- Mathematics - Lecturer in Algebra
Person: Academic

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AU - Raman, Dhruva V

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N2 - 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.

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VL - 9

SP - 30

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JO - Journal of Algebraic Statistics

JF - Journal of Algebraic Statistics

IS - 1

ER -

The Geometry of Sloppiness

Abstract

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Emilie Sonia Dufresne

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