Date/Time
Date(s) – 08/02/2017
3:00 pm – 4:00 pm
Location
VG02
Categories
The Geometry of Sloppiness
Abstract
Mathematical models in the sciences often require the estimation of unknown parameter values from data. Sloppiness provides information about the uncertainty of this task. 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 the natural metric on parameter space. This opens up alternative quantification of sloppiness beyond the traditional use of the Fisher Information Matrix, which implicitly assumes infinitesimal measurement error.
We illustrate the various concepts involved in the proper definition of sloppiness with examples of ordinary differential equation models with time series data. We also highlight the links with invariant theory and the notion of separating set.
(joint with Heather Harrington and Dhruva Raman)