  This manuscript puts forward novel practicable spatiotemporal Bayesian factor
analysis frameworks computationally feasible for moderate to large data. Our
models exhibit significantly enhanced computational scalability and storage
efficiency, deliver high overall modeling performances, and possess powerful
inferential capabilities for adequately predicting outcomes at future time
points or new spatial locations and satisfactorily clustering spatial locations
into regions with similar temporal trajectories, a frequently encountered
crucial task. We integrate on top of a baseline separable factor model with
temporally dependent latent factors and spatially dependent factor loadings
under a probit stick breaking process (PSBP) prior a new slice sampling
algorithm that permits unknown varying numbers of spatial mixture components
across all factors and guarantees them to be non-increasing through the MCMC
iterations, thus considerably enhancing model flexibility, efficiency, and
scalability. We further introduce a novel spatial latent nearest-neighbor
Gaussian process (NNGP) prior and new sequential updating algorithms for the
spatially varying latent variables in the PSBP prior, thereby attaining high
spatial scalability. The markedly accelerated posterior sampling and spatial
prediction as well as the great modeling and inferential performances of our
models are substantiated by our simulation experiments.
