  Geographically weighted regression (GWR) models handle geographical
dependence through a spatially varying coefficient model and have been widely
used in applied science, but its general Bayesian extension is unclear because
it involves a weighted log-likelihood which does not imply a probability
distribution on data. We present a Bayesian GWR model and show that its essence
is dealing with partial misspecification of the model. Current modularized
Bayesian inference models accommodate partial misspecification from a single
component of the model. We extend these models to handle partial
misspecification in more than one component of the model, as required for our
Bayesian GWR model. Information from the various spatial locations is
manipulated via a geographically weighted kernel and the optimal manipulation
is chosen according to a Kullback-Leibler (KL) divergence. We justify the model
via an information risk minimization approach and show the consistency of the
proposed estimator in terms of a geographically weighted KL divergence.
