Markov chain Monte Carlo methods for state-space models with point process observations.

Area of Science:

• Computational Statistics
• Statistical Modeling
• Time Series Analysis

Background:

• State-space models are crucial for analyzing sequential data, especially physiological signals.
• Point process observations are common in biological and physical systems.
• Efficient parameter estimation and inference are vital for accurate model interpretation.

Purpose of the Study:

• To evaluate the efficacy of various modern Markov chain Monte Carlo (MCMC) methods for parameter estimation in state-space models with point process observations.
• To compare the performance of Riemannian manifold Hamiltonian Monte Carlo (RMHMC) against a variational Bayes method.
• To assess the scalability and accuracy of these methods on both synthetic and experimental datasets.

Main Methods:

• Application of multiple Markov chain Monte Carlo (MCMC) algorithms, including Riemannian manifold Hamiltonian Monte Carlo (RMHMC).
• Parameter estimation and inference conducted on state-space models featuring point process observations.
• Comparative analysis using synthetic data for efficiency quantification and experimental data for real-world performance assessment.

Main Results:

• The Riemannian manifold Hamiltonian Monte Carlo (RMHMC) method demonstrated superior efficiency compared to other tested MCMC techniques on synthetic data.
• RMHMC exhibited comparable performance to variational Bayes methods on large experimental datasets.
• RMHMC showed superior performance over variational Bayes on smaller experimental datasets.

Conclusions:

• Modern MCMC methods, especially RMHMC, offer a powerful toolkit for inference in complex state-space models with point process data.
• RMHMC provides a robust and efficient alternative for parameter estimation, particularly advantageous for smaller datasets.
• This study validates the utility of advanced MCMC algorithms in physiological signal analysis.