  The geographically weighted regression (GWR) is a well-known statistical
approach to explore spatial non-stationarity of the regression relationship in
spatial data analysis. In this paper, we discuss a Bayesian recourse of GWR.
Bayesian variable selection based on spike-and-slab prior, bandwidth selection
based on range prior, and model assessment using a modified deviance
information criterion and a modified logarithm of pseudo-marginal likelihood
are fully discussed in this paper. Usage of the graph distance in modeling
areal data is also introduced. Extensive simulation studies are carried out to
examine the empirical performance of the proposed methods with both small and
large number of location scenarios, and comparison with the classical
frequentist GWR is made. The performance of variable selection and estimation
of the proposed methodology under different circumstances are satisfactory. We
further apply the proposed methodology in analysis of a province-level
macroeconomic data of 30 selected provinces in China. The estimation and
variable selection results reveal insights about China's economy that are
convincing and agree with previous studies and facts.
