Joining Forces of Bayesian and Frequentist Methodology: A Study for Inference in the Presence of Non-Identifiability

TL;DR

This paper explores combining Bayesian and frequentist methods to improve statistical inference in complex, high-dimensional models with non-identifiability, demonstrating a practical approach using cell biology data.

Contribution

It introduces a pragmatic framework that integrates Bayesian and frequentist techniques to address non-identifiability in complex models, enhancing uncertainty assessment.

Findings

Combined approach improves uncertainty quantification.

Profile likelihood helps identify non-identifiability.

Bayesian methods become feasible after constraining the model.

Abstract

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take advantage of both Bayesian and frequentist methods. The elegance of Bayesian methodology is founded in the propagation of information content provided by experimental data and prior assumptions to the posterior probability distribution of model predictions. However, for complex applications experimental data and prior assumptions potentially constrain the posterior probability distribution insufficiently. In these situations Bayesian Markov chain Monte Carlo sampling can be infeasible. From a frequentist point of view insufficient experimental data and prior assumptions can be interpreted as non-identifiability. The profile likelihood approach offers to detect and to resolve non-identifiability by experimental design iteratively. Therefore, it allows one to better constrain the posterior probability distribution until Markov chain Monte Carlo sampling can be used securely. Using an application from cell biology we compare both methods and show that a successive application of both methods facilitates a realistic assessment of uncertainty in model predictions.