MCMC Methods for Parameter Inference in Structurally Nonidentifiable Models

2026-07-14

AI Summary

This study addresses the challenge of parameter inference in ordinary differential equation models arising from structural non-identifiability. It introduces, for the first time, an explicit integration of structural identifiability analysis into the design of Markov chain Monte Carlo (MCMC) algorithms, proposing two novel sampling strategies: one constructs efficient proposals both within and orthogonal to the non-identifiable manifold, while the other performs inference in a low-dimensional space of identifiable parameter combinations and subsequently reconstructs the full parameter vector. By combining geometric MCMC with pseudo-marginal MCMC techniques, the method establishes a Bayesian inference framework tailored to equivalence solution manifolds. This approach significantly enhances sampling efficiency and convergence speed compared to standard MCMC methods, while preserving posterior correctness and chain ergodicity.

Abstract

We consider the problem of parameter inference for ordinary differential equation (ODE) models with structural non-identifiability. Such models arise in a wide range of scientific fields, including control theory, systems biology, and public health. Structural non-identifiability occurs when distinct parameter values provide identical model outputs, resulting in lower-dimensional manifolds of observationally equivalent solutions in the parameter space. This poses challenges for Bayesian inference and Markov chain Monte Carlo (MCMC) methods, often leading to poor mixing and slow convergence. We develop two MCMC methods that use information from structural identifiability analysis. The first, Identifiability-Aware Geometric MCMC, constructs proposals that move within and between non-identifiable manifolds. The second, Identifiability-Aware Pseudo-Marginal MCMC, performs inference on the space of identifiable parameter combinations and reconstructs full parameter values. We show that both methods target the correct posterior distribution and are ergodic under standard conditions. Numerical examples demonstrate improved sampling efficiency and convergence compared with standard MCMC methods.

Problem

• structural non-identifiability
• parameter inference
• ODE models
• Bayesian inference
• MCMC

Innovation

• structural non-identifiability
• Markov chain Monte Carlo
• parameter inference
• identifiability-aware
• ODE models