  We propose a probabilistic model for refining coarse-grained spatial data by
utilizing auxiliary spatial data sets. Existing methods require that the
spatial granularities of the auxiliary data sets are the same as the desired
granularity of target data. The proposed model can effectively make use of
auxiliary data sets with various granularities by hierarchically incorporating
Gaussian processes. With the proposed model, a distribution for each auxiliary
data set on the continuous space is modeled using a Gaussian process, where the
representation of uncertainty considers the levels of granularity. The
fine-grained target data are modeled by another Gaussian process that considers
both the spatial correlation and the auxiliary data sets with their
uncertainty. We integrate the Gaussian process with a spatial aggregation
process that transforms the fine-grained target data into the coarse-grained
target data, by which we can infer the fine-grained target Gaussian process
from the coarse-grained data. Our model is designed such that the inference of
model parameters based on the exact marginal likelihood is possible, in which
the variables of fine-grained target and auxiliary data are analytically
integrated out. Our experiments on real-world spatial data sets demonstrate the
effectiveness of the proposed model.
