Title: Spatial Regression and the Bayesian Filter,
Abstract: Regression for spatially dependent outcomes poses many challenges, for
inference and for computation. Non-spatial models and traditional spatial
mixed-effects models each have their advantages and disadvantages, making it
difficult for practitioners to determine how to carry out a spatial regression
analysis. We discuss the data-generating mechanisms implicitly assumed by
various popular spatial regression models, and discuss the implications of
these assumptions. We propose Bayesian spatial filtering as an approximate
middle way between non-spatial models and traditional spatial mixed models. We
show by simulation that our Bayesian spatial filtering model has several
desirable properties and hence may be a useful addition to a spatial
statistician's toolkit.