Bayesian Learning in a Nonlinear Multiscale State-Space Model
This work addresses modeling challenges in fields like development and heredity where processes at different temporal scales interact, though it appears incremental as it builds on existing state-space and Bayesian methods.
The authors tackled the problem of modeling multiscale interactions in complex systems by introducing a novel multiscale state-space model with feedback, using a Bayesian learning framework to estimate unknown states and process noise covariances, and demonstrated its efficacy through simulations.
The ubiquity of multiscale interactions in complex systems is well-recognized, with development and heredity serving as a prime example of how processes at different temporal scales influence one another. This work introduces a novel multiscale state-space model to explore the dynamic interplay between systems interacting across different time scales, with feedback between each scale. We propose a Bayesian learning framework to estimate unknown states by learning the unknown process noise covariances within this multiscale model. We develop a Particle Gibbs with Ancestor Sampling (PGAS) algorithm for inference and demonstrate through simulations the efficacy of our approach.