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

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 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.

Automated summary

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. It identifies stiff parameter combinations affecting the model-data fit, and reveals which of these combinations are primarily influenced by the data or the priors. The technique is beneficial in contexts where data is limited compared to the number of model parameters, and has applications in biochemistry, ecology, and cardiac electrophysiology. It also helps uncover controlling mechanisms and guide parameter prioritization for improved parameter inference.