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

Abstract: We propose a novel blocked version of the continuous-time bouncy particle sampler of Bouchard-Côté et al. (J Am Stat Assoc 113(522):855–867, 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. in Biometrika 104(4):953–969, 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. (J R Stat Soc Ser B Stat Methodol 72(3):269–342, 2010), is illustrated numerically for both simulated data and a challenging real-world financial dataset

Cell density in the border zone around old small human brain infarcts.

Nine brain autopsy cases of small old cerebral infarcts were selected for neuropathological studies. Eight of the patients had cortical infarcts, in two cases with extension into the striate body. In one case the infarct involved the striate body only. The density of neurons and glial cells was measured in the coronal and the horizontal planes at various distances from the margin of the infarct. Corresponding counting points in the contralateral hemisphere served as control. On light microscopy, the infarcted cortex was irregularly shaped, but on serial sections the bulging parts appeared to be cut off from the infarcted tissue ("pseudo-infarct islands"). The zone of transition from infarcted to normal brain tissue was less than a few mm wide. In one patient, tomographic measurements of the cerebral blood flow (CBF) and a CT scan could be compared with the neuropathological findings. In this patient, CBF in the surroundings of the infarct was decreased despite a normal neuronal density. The study supports the traditional view held by pathologists that a sharp transition exists between infarcted and normal brain tissue and suggests that the hypoperfusion zone surrounding the region of complete infarction may be due to mechanisms other than selective loss of neurons.</jats:p