  Spatio-temporal prediction of levels of an environmental exposure is an
important problem in environmental epidemiology. Our work is motivated by
multiple studies on the spatio-temporal distribution of mobile source, or
traffic related, particles in the greater Boston area. When multiple sources of
exposure information are available, a joint model that pools information across
sources maximizes data coverage over both space and time, thereby reducing the
prediction error. We consider a Bayesian hierarchical framework in which a
joint model consists of a set of submodels, one for each data source, and a
model for the latent process that serves to relate the submodels to one
another. If a submodel depends on the latent process nonlinearly, inference
using standard MCMC techniques can be computationally prohibitive. The
implications are particularly severe when the data for each submodel are
aggregated at different temporal scales. To make such problems tractable, we
linearize the nonlinear components with respect to the latent process and
induce sparsity in the covariance matrix of the latent process using compactly
supported covariance functions. We propose an efficient MCMC scheme that takes
advantage of these approximations. We use our model to address a temporal
change of support problem whereby interest focuses on pooling daily and
multiday black carbon readings in order to maximize the spatial coverage of the
study region.
