000			01814 am a22002173u 4500
042			_adc
100	1	0	_aLiu, Yang _eauthor _92539
700	1	0	_aGoudie, Robert J. B. _eauthor _92540
245	0	0	_aGeneralized Geographically Weighted Regression Model within a Modularized Bayesian Framework*
260			_c2023-01-01.
500			_a/pmc/articles/PMC7614111/
500			_a/pubmed/36714467
520			_aGeographically 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.
540			_a
540			_ahttps://creativecommons.org/licenses/by/4.0/This work is licensed under a CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/) International license.
546			_aen
690			_aArticle
655	7		_aText _2local
786	0		_nBayesian Anal
856	4	1	_uhttp://dx.doi.org/10.1214/22-BA1357 _zConnect to this object online.
999			_c931 _d931