🤖 AI Summary
This study addresses a key limitation of traditional latent-variable state-space models, which assume process noise is independent of the latent state and thus fail to capture state-dependent stochastic fluctuations commonly observed in biological and behavioral systems. To overcome this, the authors propose a state-coupled stochastic volatility framework that introduces a coupling parameter γ, allowing the variance of the latent process to dynamically scale with the deviation from an underlying latent equilibrium point. This work presents the first approach to modeling and identifying such coupling between latent states and process noise variance under partial observability. An efficient particle expectation-maximization algorithm, integrating guided particle filtering with backward trajectory smoothing, is developed for parameter estimation. Simulations demonstrate that the method substantially reduces parameter estimation bias under strong coupling and high observation noise, confirming its efficacy and robustness.
📝 Abstract
Latent state-space models are widely used to study partially observed dynamical systems, yet most formulations assume that process variability is independent of latent-state position. In many biological, behavioral, and physiological systems, however, variability may depend systematically on the underlying dynamical state, producing structured stochasticity that is not captured by constant-variance models. We introduce a state-coupled stochastic volatility framework in which latent process variance depends on displacement from a latent equilibrium. To estimate this relationship under partial observation, we develop a particle expectation-maximization procedure combining bootstrap particle filtering and backward trajectory smoothing. The model includes a coupling parameter, $γ$, that quantifies the strength of association between latent-state position and process variability. A large-scale simulation benchmark evaluated recovery and detection performance across varying coupling strengths, observation noise levels, trajectory lengths, and persistence regimes. The proposed framework consistently reduced recovery bias relative to an observed-state heteroskedastic proxy, with the largest improvements occurring under strong coupling. Recovery performance improved with increasing latent persistence, while detection performance remained competitive across a broad range of conditions and became increasingly advantageous as observation noise increased. Taken together, the results demonstrate that state-coupled volatility can be identified and estimated under partial observation when latent-state structure is explicitly modeled. The framework provides a practical methodological foundation for studying state-dependent variability and evaluating whether structured stochasticity contributes information about system dynamics beyond that contained in mean-state trajectories alone.