Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem

Area of Science:

• Systems biology
• Computational modeling
• Statistical inference

Background:

• Process models often involve numerous parameters requiring estimation from sparse experimental data.
• Independent analysis of related experiments can lead to suboptimal parameter inference.
• Accurate modeling is crucial for understanding complex biological systems like the human gut microbiome.

Purpose of the Study:

• To develop and demonstrate a hierarchical Bayesian approach for parameter inference in non-linear dynamic process models.
• To improve the power of inference by combining data from multiple related experiments.
• To generate predictive models that quantify parameter uncertainty and extend to unobserved scenarios.

Main Methods:

• Utilized a hierarchical Bayesian framework to integrate data from multiple experiments.
• Applied the method to a simulation study and experimental data from human gut microbial ecosystems.
• Developed a predictive model incorporating uncertainty quantification.

Main Results:

• The hierarchical Bayesian approach yielded more powerful inference compared to independent analysis.
• A predictive model was successfully generated, reflecting parameter uncertainty.
• The model was extended to explore conditions not directly studied experimentally.

Conclusions:

• Hierarchical Bayesian modeling offers a robust framework for parameter inference in complex systems with limited data.
• Integrating data across related experiments significantly improves model predictive power and uncertainty estimation.
• This methodology facilitates the exploration of system behaviors beyond direct experimental observation.