APT-MCMC, a C++/Python implementation of Markov Chain Monte Carlo for parameter identification.

Area of Science:

• Computational Science
• Applied Mathematics
• Biophysics

Background:

• Parameter fitting for ordinary differential equation (ODE) systems is a challenging nonlinear and multimodal inverse problem.
• Gradient-based optimizers struggle with local minima inherent in these complex systems.
• Markov Chain Monte Carlo (MCMC) methods offer a robust alternative for exploring complex parameter spaces.

Purpose of the Study:

• To introduce APT-MCMC, a novel computational tool for efficient ODE parameter estimation.
• To leverage advanced MCMC techniques for improved simulation efficiency and accuracy.
• To provide probability distributions for ODE parameters, enabling thorough analysis of model uncertainty and correlations.

Main Methods:

• Development of APT-MCMC, integrating affine-invariant ensemble sampling and parallel tempering MCMC.
• Implementation of ODE simulations in Python, compiled to C++ for performance.
• Application of Bayesian inference to estimate parameter probability distributions.
• Analysis of MCMC hyperparameters including temperature, ensemble size, step size, and swap frequency.

Main Results:

• APT-MCMC demonstrates a 20×-60× speedup compared to the emcee package for ODE parameter fitting.
• Achieved significant performance gains with a modest 14% increase in memory usage.
• Identified key MCMC hyperparameters influencing simulation efficiency.
• Provided heuristic guidelines for optimal hyperparameter tuning.

Conclusions:

• APT-MCMC offers a highly efficient and effective solution for the challenging inverse problem of ODE parameter fitting.
• The method successfully navigates multimodal landscapes and provides robust parameter probability distributions.
• The developed heuristic guidelines facilitate practical application and optimization of APT-MCMC.