A practical identifiability criterion leveraging weak-form parameter estimation

Area of Science:

• Systems Biology
• Mathematical Modeling
• Parameter Estimation

Background:

• Assessing the practical identifiability of parameters in dynamic systems is crucial for reliable model analysis.
• Existing identifiability criteria often fail to fully account for the impact of noise on parameter estimation quality.
• Computational efficiency in parameter estimation is a significant challenge, especially for complex systems.

Purpose of the Study:

• To introduce a novel practical identifiability criterion, (e, q)-identifiability, that incorporates noise levels and estimator error.
• To develop and validate a computationally efficient parameter estimation method for systems with unobserved variables.
• To demonstrate the robustness and speed of the proposed method using biological modeling examples.

Main Methods:

• Defined (e, q)-identifiability based on noise parameter (e) and mean-square error (q).
• Employed differential algebra to generate weak-form input-output equations.
• Applied Weak form Estimation of Nonlinear Dynamics (WENDy) for parameter estimation in systems with unobserved variables.

Main Results:

• The (e, q)-identifiability criterion effectively captures the impact of data noise on parameter estimate quality.
• The weak-form equation error-based method provides a significantly faster assessment of practical identifiability compared to output error methods.
• The WENDy approach demonstrated computational efficiency and robustness to noise in biological modeling scenarios.

Conclusions:

• The proposed (e, q)-identifiability criterion offers a more comprehensive assessment of parameter estimation reliability.
• The integration of differential algebra and WENDy provides an efficient and robust tool for practical identifiability analysis.
• This approach facilitates more reliable model development and analysis in complex biological systems.