Beyond data: leveraging non-empirical information and expert knowledge in Bayesian model calibration

TL;DR

This paper presents a statistical framework that incorporates expert knowledge and non-empirical information into Bayesian model calibration, enhancing model realism and predictive accuracy beyond data-driven methods.

Contribution

It introduces a novel approach for integrating non-empirical insights into Bayesian calibration, demonstrated through applications in ecology, biology, and medicine.

Findings

Non-empirical information improves model constraints.

Expert knowledge leads to more realistic model dynamics.

Framework enhances predictive accuracy over data-only calibration.

Abstract

Mathematical models connect theory with the real world through data, enabling us to interpret, understand, and predict complex phenomena. However, scientific knowledge often extends beyond what can be empirically measured, offering valuable insights into complex and uncertain systems. Here, we introduce a statistical framework for calibrating mathematical models using non-empirical information. Through examples in ecology, biology, and medicine, we demonstrate how expert knowledge, scientific theory, and qualitative observations can meaningfully constrain models. In each case, these non-empirical insights guide models toward more realistic dynamics and more informed predictions than empirical data alone could achieve. Now, our understanding of the systems represented by mathematical models is not limited by the data that can be obtained; they instead sit at the edge of scientific understanding.