Estimability Analysis

After estimating the model parameters with their associated uncertainty, as demonstrated in the Parmest Quick Start Guide and Uncertainty Quantification Sections, estimability analysis is required to identify parameters that cannot be reliably estimated from the available data due to limitations in the mathematical model structure. If such parameters exist, the model may need to be reformulated, replaced with an alternative structure, or augmented with additional prior information. In parmest, estimability analysis can be performed using eigen-decomposition of the parameter covariance matrix, profile likelihood methods, or multi-start initialization routines.

Eigen-decomposition

The estimability of model parameters can be analyzed through eigen-decomposition of the covariance matrix obtained from parameter estimation. This covariance matrix quantifies parameter uncertainty and captures both parameter variances and correlations. Eigen-decomposition of this matrix identifies principal directions in parameter space along which uncertainty is largest or smallest. These directions provide insight into parameter identifiability and reveal combinations of parameters that are either structurally identifiable or non-identifiable based on the underlying model formulation.

Note

Detailed descriptions and example code for this method will be added in a future update.

Profile Likelihood

Profile likelihood analysis evaluates parameter estimability by systematically varying one parameter while re-optimizing the remaining parameters to maintain consistency with the model and observed data. This approach is closely related to likelihood ratio–based uncertainty quantification and provides a robust characterization of practical identifiability through the shape of the likelihood surface. In addition, it can reveal structural non-identifiability when flat or unbounded profiles indicate parameter combinations that are not uniquely determined by the model formulation, particularly in nonlinear systems.

Note

Detailed descriptions and example code for this method will be added in a future update.

Multi-start Initialization

Multi-start initialization assesses parameter estimability by exploring a range of initial guesses. Because parameter estimation problems are often nonlinear and may exhibit multiple local minima, different initializations can lead to different parameter estimates. By solving the estimation problem from multiple starting points, one can evaluate the robustness of the solution and identify potential issues related to non-convexity or non-identifiability. Consistent convergence to a unique solution across initializations suggests that the parameters are structurally identifiable within the model formulation, whereas sensitivity to initialization indicates potential estimability issues.

Note

Detailed descriptions and example code for this method will be added in a future update.