Sloppiness: fundamental study, new formalism and its application in model assessment

On 20 February, 2023

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, particularly related to its quantification, and practical implications in system 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, for linear predictors. Finally, we demonstrate the proposed formalism and methods on multiple models, including those widely used in systems biology.

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