Bayesian Learning in a Nonlinear Multiscale State-Space Model

TL;DR

This paper introduces a Bayesian multiscale state-space model with a novel inference algorithm to analyze complex systems with interactions across multiple time scales, demonstrating its effectiveness through simulations.

Contribution

It presents a new multiscale state-space model combined with a Bayesian learning framework and a PGAS algorithm for efficient inference in complex multiscale systems.

Findings

Effective estimation of unknown states and noise covariances.

Successful demonstration through simulation studies.

Enhanced understanding of multiscale interactions.

Abstract

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.