🤖 AI Summary
This work addresses the challenge of parameter non-identifiability in biological systems modeling, which often induces bias in conventional estimates of model evidence and leads to erroneous model selection. The authors propose a Bayesian model evidence estimation method based on Adaptive Multiple Importance Sampling (AMIS), marking its first application to model selection under non-identifiable parameters. By integrating Bayesian inference with an efficient sampling strategy, the approach achieves comparable or superior selection accuracy to Markov chain Monte Carlo (MCMC) methods at substantially lower computational cost across multiple ecological modeling case studies. In contrast, traditional approximation techniques exhibit markedly poorer performance, thereby demonstrating the dual advantages of the proposed method in both reliability and computational efficiency.
📝 Abstract
Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple competing models, model uncertainty should be accounted for when performing inference based on available data. Bayesian model selection is a framework for testing mechanistic hypotheses and generating predictions under model uncertainty, which generally requires computation of the model evidence. In this work, we investigate the reliability of evidence computation methods when parameter non-identifiability -- the inability to distinguish between parameter values given available data -- is present, and find that deterministic evidence approximations can produce misleading model selection results because their underlying assumptions are violated. We propose a novel implementation of adaptive multiple importance sampling for evidence estimation, and demonstrate its robustness against non-identifiability. We use ecological case studies to demonstrate how simple model selection methods fail to produce accurate results, whereas our method yields model selection results that are comparable to those obtained by Markov chain Monte Carlo methods at substantially lower computational cost. Given the pervasiveness of parameter non-identifiability in mathematical biology, this work provides a practical approach to reliable model selection in the presence of poorly identified parameters.