Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal...

Area of Science:

• Computational Statistics
• Dynamical Systems Modeling
• Machine Learning

Background:

• Understanding dynamic systems requires extracting latent nonlinear dynamics from time-series data.
• State space models are probabilistic graphical models crucial for time-series analysis, but parameter estimation is challenging.
• The particle marginal Metropolis-Hastings (PMMH) method estimates parameters but suffers from practical initial value dependence.

Purpose of the Study:

• To address the initial value dependence limitations of the PMMH method in state space models.
• To develop an improved parameter estimation technique for latent nonlinear dynamics.
• To enhance the efficiency of parameter sampling in complex dynamic systems.

Main Methods:

• Proposed the replica exchange particle marginal Metropolis-Hastings (REPMMH) method, combining PMMH with replica exchange.
• Simultaneously performs global search at high temperatures and local fine search at low temperatures.
• Evaluated using simulated data from the Izhikevich neuron model and Lévy-driven stochastic volatility model.

Main Results:

• The REPMMH method significantly improves upon the PMMH method by mitigating initial value dependence.
• Demonstrated more efficient and robust parameter sampling in state space models compared to existing methods.
• Successfully applied to complex models, including neural dynamics and stochastic volatility.

Conclusions:

• The REPMMH method offers a superior approach for parameter estimation in state space models.
• This technique enables more reliable extraction of latent nonlinear dynamics from time-series data.
• REPMMH provides a powerful tool for analyzing complex dynamic systems in various scientific fields.