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The geographically weighted regression (GWR) is a well-known statistical approach to explore spatial non-stationarity of the regression relationship in spatial data analysis. In this paper, we discuss a Bayesian recourse of GWR. Bayesian…

Applications · Statistics 2020-07-07 Zhihua Ma , Yishu Xue , Guanyu Hu

Spatial statistical models are commonly used in geographical scenarios to ensure spatial variation is captured effectively. However, spatial models and cluster algorithms can be complicated and expensive. This paper pursues three main…

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…

Methodology · Statistics 2026-03-18 Yang Liu , Robert J. B. Goudie

Geographically weighted regression (GWR) is a popular tool for modeling spatial heterogeneity in a regression model. However, the current weighting function used in GWR only considers the geographical distance, while the attribute…

Machine Learning · Computer Science 2023-05-17 Hone-Jay Chu , Po-Hung Chen , Sheng-Mao Chang , Muhammad Zeeshan Ali , Sumriti Ranjan Patra

Although geographically weighted Poisson regression (GWPR) is a popular regression for spatially indexed count data, its development is relatively limited compared to that found for linear geographically weighted regression (GWR), where…

This article focuses on the use of Geographically Weighted Regression (GWR) method to correct air quality low-cost sensors measurements. Those sensors are of major interest in the current era of high-resolution air quality monitoring at…

Applications · Statistics 2026-03-30 Jean-Michel Poggi , Bruno Portier , Emma Thulliez

Although a number of studies have developed fast geographically weighted regression (GWR) algorithms for large samples, none of them has achieved linear-time estimation, which is considered a requisite for big data analysis in machine…

Methodology · Statistics 2020-04-24 Daisuke Murakami , Narumasa Tsutsumida , Takahiro Yoshida , Tomoki Nakaya , Binbin Lu

It is widely known that geographically weighted regression(GWR) is essentially same as varying-coefficient model. In the former research about varying-coefficient model, scholars tend to use multidimensional-kernel-based locally weighted…

Econometrics · Economics 2018-04-13 Zihao Yuan

Geographical and Temporal Weighted Regression (GTWR) model is an important local technique for exploring spatial heterogeneity in data relationships, as well as temporal dependence due to its high fitting capacity when it comes to real…

Methodology · Statistics 2023-09-21 Héctor Araya , Lisandro Fermín , Silfrido Gómez , Tania Roa , Soledad Torres

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

Applications · Statistics 2018-08-07 Donald R. Williams , Juho Piironen , Aki Vehtari , Philippe Rast

Geographically Weighted Regression (GWR) is increasingly used in spatial analyses of social and environmental data. It allows spatial heterogeneities in processes and relationships to be investigated through a series of local regression…

Local spatial models such as Geographically Weighted Regression (GWR) and Multiscale Geographically Weighted Regression (MGWR) serve as instrumental tools to capture intrinsic contextual effects through the estimates of the local intercepts…

Geographically Weighted Regression (GWR) is a widely recognized technique for modeling spatial heterogeneity. However, it is commonly assumed that the relationships between dependent and independent variables are linear. To overcome this…

Machine Learning · Computer Science 2025-04-08 Jianfei Cao , Dongchao Wang

Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…

Machine Learning · Computer Science 2014-02-05 Franziska Meier , Philipp Hennig , Stefan Schaal

The first law of geography is a cornerstone of spatial analysis, emphasizing that nearby and related locations tend to be more similar, however, defining what constitutes "near" and "related" remains challenging, as different phenomena…

Methodology · Statistics 2026-02-02 M. Naser Lessani , Zhenlong Li , Manzhu Yu , Helen Greatrex , Chan Shen

Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed…

Methodology · Statistics 2021-06-08 Isa Marques , Thomas Kneib , Nadja Klein

Inductive bias is a key factor in spatial regression models, determining how well a model can learn from limited data and capture spatial patterns. This work revisits the inductive biases in Geographically Neural Network Weighted Regression…

Machine Learning · Computer Science 2025-07-23 Zhenyuan Chen

Model averaging methods have become an increasingly popular tool for improving predictions and dealing with model uncertainty, especially in Bayesian settings. Recently, frequentist model averaging methods such as information theoretic and…

Econometrics · Economics 2024-04-18 Kevin Huynh

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…

Methodology · Statistics 2017-11-06 Zemei Xu , Daniel F. Schmidt , Enes Makalic , Guoqi Qian , John L. Hopper

Confronted with the spatial heterogeneity of real estate market, some traditional research utilized Geographically Weighted Regression (GWR) to estimate the house price. However, its kernel function is non-linear, elusive, and complex to…

Applications · Statistics 2022-02-10 Zimo Wang , Yicheng Wang , Sensen Wu
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