Abstract
Precise estimation of parameters in a complex dynamical system is often challenging, even if provided with adequate quality and quantity of data. A major challenge is the possible presence of large regions in the parameter space over which model predictions are nearly identical. This property, known as sloppiness, has been reasonably well-addressed in the past decade, studying its possible impacts and remedies. However, certain critical unanswered questions concerning sloppiness, its quantification and practical implications in identification still prevail. In this work, we systematically examine sloppiness at a fundamental level and formalise a new theoretical definition of sloppiness. Further, we propose a method to quantify sloppiness for non-linear predictors. The proposed method aids in the characterisation of a model structure around a point of interest in the parameter space and detecting local structural unidentifiability. Further, we establish a mathematical relationship between practical identifiability and sloppiness in linear predictors. Finally, we demonstrate the proposed formalism and methods on standard models.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
↵* kraman{at}iitm.ac.in, arunkt{at}iitm.ac.in
