  We introduce a Bayesian non-parametric spatial factor analysis model with
spatial dependency induced through a prior on factor loadings. For each column
of the loadings matrix, spatial dependency is encoded using a probit
stick-breaking process (PSBP) and a multiplicative gamma process shrinkage
prior is used across columns to adaptively determine the number of latent
factors. By encoding spatial information into the loadings matrix, meaningful
factors are learned that respect the observed neighborhood dependencies, making
them useful for assessing rates over space. Furthermore, the spatial PSBP prior
can be used for clustering temporal trends, allowing users to identify regions
within the spatial domain with similar temporal trajectories, an important task
in many applied settings. In the manuscript, we illustrate the model's
performance in simulated data, but also in two real-world examples:
longitudinal monitoring of glaucoma and malaria surveillance across the
Peruvian Amazon. The R package spBFA, available on CRAN, implements the method.
