A Systematic Computational Framework for Practical Identifiability Analysis in Mathematical Models Arising from Biology

TL;DR

This paper introduces a comprehensive computational framework for practical identifiability analysis in biological models, improving efficiency and reliability in parameter estimation and experimental design.

Contribution

It presents a novel framework linking practical identifiability to Fisher Information Matrix invertibility and introduces new metrics and regularization methods for better analysis.

Findings

Framework effectively evaluates parameter identifiability in biological models.

New metrics simplify and speed up identifiability assessment.

Application demonstrates improved model reliability and experimental guidance.

Abstract

Practical identifiability is a critical concern in data-driven modeling of mathematical systems. In this paper, we propose a novel framework for practical identifiability analysis to evaluate parameter identifiability in mathematical models of biological systems. Starting with a rigorous mathematical definition of practical identifiability, we demonstrate its equivalence to the invertibility of the Fisher Information Matrix. Our framework establishes the relationship between practical identifiability and coordinate identifiability, introducing a novel metric that simplifies and accelerates the evaluation of parameter identifiability compared to the profile likelihood method. Additionally, we introduce new regularization terms to address non-identifiable parameters, enabling uncertainty quantification and improving model reliability. To guide experimental design, we present an optimal data collection algorithm that ensures all model parameters are practically identifiable. Applications to Hill functions, neural networks, and dynamic biological models demonstrate the feasibility and efficiency of the proposed computational framework in uncovering critical biological processes and identifying key observable variables.