Comparing Bayesian and frequentist inference in biological models: A comparative analysis of accuracy, uncertainty, and identifiability.

Mathematical models are widely used to study ecological and epidemiological systems, but the accuracy of the resulting inferences and forecasts depends on the estimation framework. This study compares Bayesian and frequentist approaches across three biological models using four datasets: The Lotka-Volterra predator-prey system, a generalized logistic model (GLM) applied to lung injury and mpox data, and the susceptible-exposed-infected (reported and unreported)-recovered (SEIUR) epidemic model for COVID-19. To ensure a fair comparison, both approaches were implemented with a normal error structure. We first examined the structural identifiability to determine which parameters can be recovered in principle. We then evaluated practical identifiability and fitting performance using four metrics: Mean absolute error, mean squared error, prediction interval coverage, and the weighted interval score. For the Lotka-Volterra model, we studied three types of observations: Prey only, predator only, and both species together. The frequentist workflow, implemented through QuantDiffForecast, uses nonlinear least squares and parametric bootstraping to quantify uncertainty. The Bayesian workflow, implemented through BayesianFitForecast, uses Hamiltonian Monte Carlo sampling to obtain posterior distributions and diagnostic measures. Our results show that frequentist inference performs well when the system comprises fully observed data, as in the GLM or in the Lotka-Volterra model when both species are observed. Bayesian inference performs better when uncertainty is high and observations are limited or indirect, as seen in the SEIUR epidemic model. The identifiability analysis helps explain these differences by showing how observability shapes the reliability of parameter recovery and uncertainty quantification.