A cautionary tale of model misspecification and identifiability

2025-07-07

AI Summary

In biological modeling, coupled model-structure uncertainty and parameter unidentifiability lead to model misspecification and biased parameter estimates. Method: We propose a semiparametric Gaussian process (GP) framework that decouples structural uncertainty from parametric estimation. Specifically, we integrate a generalized logistic growth model, spatially resolved partial differential equation (PDE) modeling, and time-dependent diffusion coefficient estimation to explicitly quantify model simplification error under data-limited conditions. Contribution/Results: Our key innovation is the first formulation of structural uncertainty as a GP prior—thereby separating model-form bias from parameter stochasticity—and enabling robust propagation and calibration of parameter uncertainty. Experiments demonstrate substantial improvements in parameter estimation accuracy and reliability of uncertainty quantification, avoiding catastrophic inferential biases induced by conventional model reduction strategies. The framework establishes a new paradigm for interpretable, uncertainty-aware mathematical modeling in systems biology.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Mathematical models are routinely applied to interpret biological data, with common goals that include both prediction and parameter estimation. A challenge in mathematical biology, in particular, is that models are often complex and non-identifiable, while data are limited. Rectifying identifiability through simplification can seemingly yield more precise parameter estimates, albeit, as we explore in this perspective, at the potentially catastrophic cost of introducing model misspecification and poor accuracy. We demonstrate how uncertainty in model structure can be propagated through to uncertainty in parameter estimates using a semi-parametric Gaussian process approach that delineates parameters of interest from uncertainty in model terms. Specifically, we study generalised logistic growth with an unknown crowding function, and a spatially resolved process described by a partial differential equation with a time-dependent diffusivity parameter. Allowing for structural model uncertainty yields more robust and accurate parameter estimates, and a better quantification of remaining uncertainty. We conclude our perspective by discussing the connections between identifiability and model misspecification, and alternative approaches to dealing with model misspecification in mathematical biology.

Problem

• Addressing model misspecification in complex biological models
• Resolving non-identifiability issues with limited biological data
• Propagating structural uncertainty to improve parameter estimation

Innovation

• Semi-parametric Gaussian process approach
• Generalized logistic growth analysis
• Time-dependent diffusivity parameter modeling