Analysis of sloppiness in model simulations: unveiling parameter uncertainty when mathematical models are fitted to data

TL;DR

This paper presents a new method to analyze parameter sensitivity and uncertainty in complex models, especially when data is limited, helping to identify key parameters and guiding future experiments.

Contribution

It introduces a comprehensive approach to distinguish between data-informed and prior-influenced parameter combinations in model fitting, applicable to various scientific fields.

Findings

Identifies stiff parameter combinations affecting model fit

Reveals which parameters are data-informed versus prior-influenced

Guides experimental prioritization for better parameter inference

Abstract

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This novel approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.