  Spatial regression of random fields based on potentially biased sensing
information is proposed in this paper. One major concern in such applications
is that since it is not known a-priori what the accuracy of the collected data
from each sensor is, the performance can be negatively affected if the
collected information is not fused appropriately. For example, the data
collector may measure the phenomenon inappropriately, or alternatively, the
sensors could be out of calibration, thus introducing random gain and bias to
the measurement process. Such readings would be systematically distorted,
leading to incorrect estimation of the spatial field. To combat this
detrimental effect, we develop a robust version of the spatial field model
based on a mixture of Gaussian process experts. We then develop two different
approaches for Bayesian spatial field reconstruction: the first algorithm is
the Spatial Best Linear Unbiased Estimator (S-BLUE), in which one considers the
quadratic loss function and restricts the estimator to the linear family of
transformations; the second algorithm is based on empirical Bayes, which
utilises a two-stage estimation procedure to produce accurate predictive
inference in the presence of "misbehaving" sensors. In addition, we develop the
distributed version of these two approaches to drastically improve the
computational efficiency in large-scale settings. We present extensive
simulation results using both synthetic datasets and semi-synthetic datasets
with real temperature measurements and simulated distortions to draw useful
conclusions regarding the performance of each of the algorithms.
