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

2025-05-28

AI Summary

Purely data-driven Bayesian modeling often fails to capture the underlying mechanisms of complex systems due to insufficient mechanistic guidance. Method: This paper proposes a novel Bayesian model calibration framework that systematically integrates non-empirical information—such as expert knowledge, scientific theories, and qualitative observations—as formalized prior constraints. Leveraging prior encoding, qualitative constraint modeling, and multi-source information fusion, these constraints are embedded directly into the Bayesian inference pipeline, enabling synergistic constraint from both theoretical understanding and empirical data. Contribution/Results: Compared with conventional approaches, the framework significantly expands the class of calibratable models. Case studies in ecology, biology, and medicine demonstrate improved dynamic plausibility, higher predictive confidence, and greater consistency with established scientific knowledge. By bridging theory and data, the method advances Bayesian modeling beyond mere “data fitting” toward “mechanistically credible” inference.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Incorporating non-empirical information into Bayesian model calibration
• Enhancing model accuracy using expert knowledge and qualitative insights
• Overcoming data limitations with scientific theory and expert guidance

Innovation

• Bayesian model calibration with non-empirical data
• Integrating expert knowledge into statistical frameworks
• Enhancing predictions using qualitative observations