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Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework.

Published version
Peer-reviewed

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Authors

Liu, Yang 
Goudie, Robert JB 

Abstract

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.

Description

Keywords

62J12, Primary 62F15, cutting feedback, geographically weighted regression, model misspecification, modularized Bayesian, power likelihood

Journal Title

Bayesian Anal

Conference Name

Journal ISSN

1936-0975
1931-6690

Volume Title

Publisher

Institute of Mathematical Statistics
Sponsorship
MRC (unknown)
Yang Liu was supported by a Cambridge International Scholarship from the Cambridge Com- monwealth, European and International Trust. Robert J. B. Goudie was funded by the UK Medical Research Council [programme code MC UU 00002/2].