In the quantitative Geography literature, particularly in Geographical Information Sciences, the concepts of location error and attribute
error are firmly established. What to do about these sources of error has often been handled separately and not always statistically. In the
geostatistics literature, attribute error is referred to as “regional variability” or “spatial variability,” and it is often assumed that there is no
location error. The article by Fanshawe and Diggle (hereafter, FD) builds on earlier work by Cressie and others on spatial statistical methods
where both spatial variability and location (equivalently, positional) error is modeled. The authors extend that approach, which was based on
empirical hierarchical modeling, to Bayesian hierarchical modeling.
Suppose Y are data, S is the process (of possibly different dimensions than Y), and θ are the parameters. The Bayesian hierarchical model
(BHM) models the joint distribution