Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems

Area of Science:

• Quantitative biology
• Computational biology
• Statistical inference

Background:

• Mathematical models are crucial for analyzing biological processes, but their parameters require estimation from experimental data.
• Markov chain Monte Carlo (MCMC) methods are increasingly used for rigorous uncertainty analysis in parameter estimation.
• A lack of comprehensive comparisons makes selecting and tuning appropriate MCMC algorithms challenging.

Purpose of the Study:

• To benchmark state-of-the-art single- and multi-chain MCMC sampling algorithms.
• To evaluate different initialization and adaptation schemes for MCMC methods.
• To provide guidance for selecting optimal MCMC algorithms in quantitative biology.

Main Methods:

• Benchmarking of Adaptive Metropolis, Delayed Rejection Adaptive Metropolis, Metropolis adjusted Langevin algorithm, Parallel Tempering, and Parallel Hierarchical Sampling.
• Consideration of various posterior distribution types arising from complex biological system features (bifurcations, chaos).
• Development of a semi-automatic pipeline for objective comparison of sampling results.

Main Results:

• Multi-chain MCMC algorithms generally demonstrate superior performance compared to single-chain algorithms.
• Performance gains are achievable with multi-chain methods, sometimes enhanced by multi-start local optimization.
• The study highlights the importance of assessing MCMC chain exploration quality before relying solely on effective sample size.

Conclusions:

• Multi-chain algorithms are recommended over single-chain methods for parameter estimation in quantitative biology.
• The developed benchmark collection can aid in evaluating novel MCMC algorithms.
• Addressing MCMC chain exploration quality is essential to prevent erroneous conclusions in data analysis.