Dataset for: Bayesian Finite Population Modeling for Spatial Process Settings

We develop a Bayesian model-based approach to finite population estimation
accounting for spatial dependence. Our innovation here is a framework that achieves
inference for finite population quantities in spatial process settings. A key distinction
from the small area estimation setting is that we analyze finite populations referenced
by their geographic coordinates (point-referenced data). Specifically, we consider a
two-stage sampling design in which the primary units are geographic regions, the
secondary units are point-referenced locations, and the measured values are assumed
to be a partial realization of a spatial process. Traditional geostatistical models do
not account for variation attributable to finite population sampling designs, which
can impair inferential performance. On the other hand, design-based estimates will
ignore the spatial dependence in the finite population. This motivates the introduction
of geostatistical processes that will enable inference at arbitrary locations in our
domain of interest.We demonstrate using simulation experiments that process-based
finite population sampling models considerably improve model fit and inference over
models that fail to account for spatial correlation. Furthermore, the process based
models offer richer inference with spatially interpolated maps over the entire region.
We reinforce these improvements and demonstrate scalable inference for groundwater
Nitrate levels in the population of California Central Valley wells by offering
estimates of mean Nitrate levels and their spatially interpolated maps.