Open Access
2023 Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework
Yang Liu, Robert J. B. Goudie
Author Affiliations +
Bayesian Anal. Advance Publication 1-36 (2023). DOI: 10.1214/22-BA1357


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.

Funding Statement

Yang Liu was supported by a Cambridge International Scholarship from the Cambridge Commonwealth, European and International Trust. Robert J. B. Goudie was funded by the UK Medical Research Council [programme code MC_UU_00002/2].


The data analysed and the code used in this study are freely available at

For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.


Download Citation

Yang Liu. Robert J. B. Goudie. "Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework." Bayesian Anal. Advance Publication 1 - 36, 2023.


Published: 2023
First available in Project Euclid: 13 January 2023

arXiv: 2106.00996
Digital Object Identifier: 10.1214/22-BA1357

Primary: 62F15 , 62J12

Keywords: cutting feedback , geographically weighted regression , model misspecification , modularized Bayesian , power likelihood

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