Comparing Bayesian and Frequentist Inference in Biological Models: A Comparative Analysis of Accuracy, Uncertainty, and Identifiability

TL;DR

This study compares Bayesian and Frequentist inference methods across various biological models, highlighting their strengths and limitations in terms of accuracy, uncertainty quantification, and parameter identifiability based on data conditions.

Contribution

It provides a comprehensive comparison of Bayesian and Frequentist approaches in biological modeling, emphasizing how data richness and observability influence their performance.

Findings

Frequentist methods perform best with rich, fully observed data.

Bayesian methods excel with sparse data and high latent-state uncertainty.

Structural identifiability analysis clarifies when parameters can be reliably estimated.

Abstract

Mathematical models support inference and forecasting in ecology and epidemiology, but results depend on the estimation framework. We compare Bayesian and Frequentist approaches across three biological models using four datasets: Lotka-Volterra predator-prey dynamics (Hudson Bay), a generalized logistic model (lung injury and 2022 U.S. mpox), and an SEIUR epidemic model (COVID-19 in Spain). Both approaches use a normal error structure to ensure a fair comparison. We first assessed structural identifiability to determine which parameters can theoretically be recovered from the data. We then evaluated practical identifiability and forecasting performance using four metrics: mean absolute error (MAE), mean squared error (MSE), 95 percent prediction interval (PI) coverage, and weighted interval score (WIS). For the Lotka-Volterra model with both prey and predator data, we analyzed three scenarios: prey only, predator only, and both. The Frequentist workflow used QuantDiffForecast (QDF) in MATLAB, which fits ODE models via nonlinear least squares and quantifies uncertainty through parametric bootstrap. The Bayesian workflow used BayesianFitForecast (BFF), which employs Hamiltonian Monte Carlo sampling via Stan to generate posterior distributions and diagnostics such as the Gelman-Rubin R-hat statistic. Results show that Frequentist inference performs best when data are rich and fully observed, while Bayesian inference excels when latent-state uncertainty is high and data are sparse, as in the SEIUR COVID-19 model. Structural identifiability clarifies these patterns: full observability benefits both frameworks, while limited observability constrains parameter recovery. This comparison provides guidance for choosing inference frameworks based on data richness, observability, and uncertainty needs.