Bayesian inference for dynamical systems.

Area of Science:

• Computational Science
• Mathematical Modeling
• Statistical Inference

Background:

• Bayesian inference is widely used for parameter estimation in dynamical systems.
• Existing methodologies lack comprehensive formalization, hindering consistent application.
• Accurate parameter estimation is crucial for understanding and predicting system behavior.

Purpose of the Study:

• To present a formalized and detailed methodology for dynamical system parameter estimation using Bayesian inference.
• To provide a structured approach encompassing various statistical techniques.
• To enhance the reliability and interpretability of parameter estimates for complex systems.

Main Methods:

• Utilizing diverse probability distributions for model parameterization.
• Implementing Markov Chain Monte Carlo (MCMC) sampling for posterior distribution approximation.
• Calculating credible intervals for parameter uncertainty quantification.
• Generating prediction intervals for model output forecasting.

Main Results:

• A comprehensive Bayesian inference methodology for dynamical systems is established.
• The approach effectively handles parameter estimation and uncertainty quantification.
• Demonstrated applicability through a logistic growth model example.

Conclusions:

• The presented methodology offers a robust framework for dynamical system parameter estimation.
• Formalized Bayesian inference improves the rigor and reproducibility of scientific modeling.
• This work provides a valuable resource for researchers in computational and statistical modeling.