Bayesian model selection for complex dynamic systems.

Area of Science:

• Complex Systems Analysis
• Statistical Modeling
• Data Science

Background:

• Time series from complex systems (e.g., financial markets, atmosphere) often exhibit superstatistical random walks.
• These walks feature simple low-level models with parameters fluctuating over time according to an unknown high-level model.

Purpose of the Study:

• To develop a computationally efficient method for inferring parameter variations in time series.
• To objectively select between competing high-level models using model evidence.
• To apply the method to diverse real-world problems.

Main Methods:

• Inference of parameter time course from time series with short-range correlations.
• Evaluation of model evidence for objective model selection.
• Application to financial markets, cancer research, occupational safety, and climate science.

Main Results:

• Successful inference of parameter variations in complex time series.
• Objective selection of appropriate high-level models.
• Demonstrated utility across finance, biology, safety, and climate forecasting.

Conclusions:

• The developed method provides an efficient and objective approach to analyze superstatistical random walks.
• This technique enhances the understanding and prediction capabilities in various scientific domains.
• It offers a robust tool for detecting anomalies and comparing complex scenarios.