Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state space models

We propose a novel blocked version of the continuous-time bouncy particle sampler of [Bouchard-C\^ot\é et al., 2018] which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state space models [Singh et al., 2017] and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the resulting algorithm. The new algorithms are particularly efficient for latent state inference in high-dimensional state space models, where blocking in both space and time is necessary to avoid degeneracy of MCMC. The efficiency of our blocked bouncy particle sampler, in comparison with both the standard implementation of the bouncy particle sampler and the particle Gibbs algorithm of Andrieu et al. [2010], is illustrated numerically for both simulated data and a challenging real-world financial dataset.