Bayesian Geographically Weighted Regression using Fused Lasso Prior

Abstract: 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.