The geometry of Sloppiness

Keywords: sloppiness, structural identifiability, inference, metric geometry


The use of mathematical models in the sciences often requires 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 and define rigorously its 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 and the measurement error is infinitesimal. Applications include parametric statistical models, explicit time dependent models, and ordinary differential equation models.

Author Biographies

Emilie Dufresne, University of Nottingham
Anne McLaren Fellow, School of Mathematical Sciences
Heather A Harrington, University of Oxford
Royal Society University Research Fellow, Mathematical Institute
Dhruva V Raman, University of Cambridge
Department of engineering


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