Statistical Modelling Approaches for Analyzing Patterns and Predicting Behavior in Complex Systems

Abstract

Understanding and predicting behaviours in complex systems is a critical challenge across various fields, including climate science, financial markets, biological systems, and epidemiology. This study evaluates classical and modern statistical modelling approaches to analyze patterns and forecast outcomes in such systems. Classical methods, such as regression analysis and time series modelling, show high interpretability (effectiveness scores of 9 and 8, respectively) but are limited in handling nonlinearity and uncertainty (scores as low as 2–4). In contrast, modern techniques like machine learning models and Bayesian networks demonstrate superior performance in managing complexity and uncertainty (scores of 7–9), though they introduce greater computational demands. Using examples from real-world applications, including General Circulation Models (GCMs) in climate science and stochastic SEIR models in epidemiology, the study highlights that higher model complexity (score 8 in climate modelling) does not always guarantee higher prediction accuracy (score 7). In contrast, moderate complexity in epidemiological models (score 6) achieves excellent predictive performance (score 9). Model selection, validation, and interpretability challenges are discussed, emphasizing the trade-offs between complexity and practical usability. This research provides new insights by systematically comparing the predictive effectiveness and challenges across different application domains. The findings suggest that hybrid and domain-informed modelling strategies offer the best potential for improving prediction and understanding in complex systems. In conclusion, effective statistical modelling requires a balanced approach, integrating domain expertise, model adaptability, and ongoing validation to maximize interpretability and predictive accuracy.