Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems.

Area of Science:

• Computational biology
• Systems biology
• Statistical modeling

Background:

• Parameter estimation for differential equation models of intracellular processes is challenging due to limited data and parameter correlation.
• Markov chain Monte Carlo (MCMC) methods are suitable but computationally expensive, with slow convergence for correlated parameters.
• Hamiltonian Monte Carlo (HMC) offers better performance but is hindered by high computational costs for trajectory calculations.

Purpose of the Study:

• To improve the efficiency of state-of-the-art Hamiltonian Monte Carlo methods for steady-state dynamical models.
• To develop a novel approach for efficiently calculating geometric quantities in HMC by tracking steady states and using local sensitivity information.

Main Methods:

• Implemented a Newton-Raphson method to track steady states along Hamiltonian trajectories.
• Utilized local sensitivity information to efficiently compute required geometric quantities.
• Compared Euclidean and Riemannian HMC on three intracellular process models using real data.

Main Results:

• Achieved at least an order of magnitude improvement in effective sampling speed for intracellular process models.
• Demonstrated the approach's applicability to other gradient-based MCMC methods, including Langevin diffusions.
• Validated the method's benefits across all tested models.

Conclusions:

• The novel approach significantly enhances the efficiency of Hamiltonian Monte Carlo methods for dynamical models.
• This improvement facilitates more robust statistical analysis and parameter estimation in systems biology.
• Open-source Matlab code for the MCMC methodology is available for broader use.