Reliable model selection in the presence of parameter non-identifiability

TL;DR

This paper introduces a robust adaptive importance sampling method for reliable Bayesian model selection in biological systems, especially when parameters are non-identifiable, outperforming traditional approaches in accuracy and efficiency.

Contribution

The authors develop a novel adaptive importance sampling technique that improves evidence estimation robustness against parameter non-identifiability in biological models.

Findings

Deterministic evidence approximations can mislead model selection due to violated assumptions.

The proposed method is robust against non-identifiability and computationally efficient.

Case studies show the method's accuracy is comparable to MCMC but with lower computational cost.

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.