  A main purpose of spatial data analysis is to predict the objective variable
for the unobserved locations. Although Geographically Weighted Regression (GWR)
is often used for this purpose, estimation instability proves to be an issue.
To address this issue, Bayesian Geographically Weighted Regression (BGWR) has
been proposed. In BGWR, by setting the same prior distribution for all
locations, the coefficients' estimation stability is improved. However, when
observation locations' density is spatially different, these methods do not
sufficiently consider the similarity of coefficients among locations. Moreover,
the prediction accuracy of these methods becomes worse. To solve these issues,
we propose Bayesian Geographically Weighted Sparse Regression (BGWSR) that uses
Bayesian Fused Lasso for the prior distribution of the BGWR coefficients.
Constraining the parameters to have the same values at adjacent locations is
expected to improve the prediction accuracy at locations with a low number of
adjacent locations. Furthermore, from the predictive distribution, it is also
possible to evaluate the uncertainty of the predicted value of the objective
variable. By examining numerical studies, we confirmed that BGWSR has better
prediction performance than the existing methods (GWR and BGWR) when the
density of observation locations is spatial difference. Finally, the BGWSR is
applied to land price data in Tokyo. Thus, the results suggest that BGWSR has
better prediction performance and smaller uncertainty than existing methods.
