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

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.

References in corpus (13)

• Universally Sloppy Parameter Sensitivities in Systems Biology
• On structural and practical identifiability
• The statistical mechanics of complex signaling networks : nerve growth factor signaling
• The geometry of nonlinear least squares with applications to sloppy models and optimization
• A Survey of Monte Carlo Methods for Parameter Estimation
• Dimension-independent likelihood-informed MCMC
• Likelihood-informed dimension reduction for nonlinear inverse problems
• The limitations of model-based experimental design and parameter estimation in sloppy systems
• Accelerating MCMC with active subspaces
• When the optimal is not the best: parameter estimation in complex biological models
• Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction
• Cause and Cure of Sloppiness in Ordinary Differential Equation Models
• Prior normalization for certified likelihood-informed subspace detection of Bayesian inverse problems