Inference on high-dimensional implicit dynamic models using a guided intermediate resampling filter.

Area of Science:

• Statistics
• Computational Science
• Dynamical Systems

Background:

• Markov process models with intractable transition densities are common in implicitly defined models.
• Existing particle filter methods struggle with the curse of dimensionality in nonlinear, non-Gaussian models.
• Ensemble Kalman filter methods offer scalability but are unsuitable for highly nonlinear or non-Gaussian dynamics.

Purpose of the Study:

• To propose a scalable particle filter method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models.
• To address the challenge of analytically intractable transition densities in such models.
• To enable likelihood-based inference for complex spatiotemporal systems.

Main Methods:

• Developed a particle filter method that propagates particles at intermediate time intervals and resamples based on forecast likelihood.
• Assumes a continuous-time latent process with an available simulator.
• Combined the particle filter with parameter estimation for likelihood-based inference.

Main Results:

• The proposed method demonstrates improved practical and theoretical scalability with respect to model dimension.
• Successfully applied the methodology to a stochastic Lorenz 96 model.
• Validated the approach on a population dynamics model for infectious diseases in a linked network.

Conclusions:

• The novel particle filter method offers a scalable solution for inference in complex, implicitly defined Markov process models.
• This approach is particularly valuable for nonlinear, non-Gaussian, and high-dimensional systems where traditional methods fail.
• The demonstrated applications highlight the method's utility in fields like climate modeling and epidemiology.