Blocked Particle Gibbs Schemes for High Dimensional Interacting Systems

This paper examines the use of blocking strategies for Particle Gibbs sampling schemes for high dimensional latent state space models with interacting components. Such strategies are particularly advantageous for high-dimensional systems because they allow multiple lower-dimensional blocks to be sampled, avoiding the curse of dimensionality within the particle filter. This paper presents algorithms for blocked Particle Gibbs sampling, as well as examining several special cases. Analogies to the bootstrap particle filter are given, along with an optimal proposal in the case of Gaussian systems with linear Gaussian observations. The paper demonstrates blocking schemes on realistic example applications: tracking multiple interacting targets and data assimilation for a nonlinear diffusion system. The effect of block size and number of particles used on computational efficiency is also examined through experiments, which demonstrate that the optimal blocking strategy is both problem and algorithm dependent and results from a compromise between the improved efficiency of blocking in Gibbs schemes and the 'curse of dimensionality' in the particle filter