🤖 AI Summary
Sampling the full posterior in high-dimensional nonlinear, non-Gaussian latent dynamic models remains challenging: particle Gibbs methods suffer from the curse of dimensionality, while Gaussian approximations (e.g., extended Kalman filtering) introduce substantial bias, compromising sampling accuracy. This paper proposes a novel auxiliary-variable MCMC framework that introduces synthetic observations as auxiliary variables, incorporates exact Kalman filtering to construct high-quality proposal distributions, and designs a time-parallelizable conditional Sequential Monte Carlo (cSMC) algorithm. Implemented on GPUs via temporal slice parallelization, the method achieves logarithmic speedup. Theoretically grounded, it significantly improves statistical accuracy and sampling efficiency in high-dimensional settings, while maintaining scalability and engineering practicality.
📝 Abstract
Sampling from the full posterior distribution of high-dimensional non-linear, non-Gaussian latent dynamical models presents significant computational challenges. While Particle Gibbs (also known as conditional sequential Monte Carlo) is considered the gold standard for this task, it quickly degrades in performance as the latent space dimensionality increases. Conversely, globally Gaussian-approximated methods like extended Kalman filtering, though more robust, are seldom used for posterior sampling due to their inherent bias. We introduce novel auxiliary sampling approaches that address these limitations. By incorporating artificial observations of the system as auxiliary variables in our MCMC kernels, we develop both efficient exact Kalman-based samplers and enhanced Particle Gibbs algorithms that maintain performance in high-dimensional latent spaces. Some of our methods support parallelisation along the time dimension, achieving logarithmic scaling when implemented on GPUs. Empirical evaluations demonstrate superior statistical and computational performance compared to existing approaches for high-dimensional latent dynamical systems.
