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Dynamic Evolution and Convergence of the Coupled and Coordinated Development of Urban-Rural Basic Education in China.

Entropy (Basel, Switzerland)·2025
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Modeling Spatial Data with Heteroscedasticity Using PLVCSAR Model: A Bayesian Quantile Regression Approach.

Rongshang Chen1,2, Zhiyong Chen3,4

  • 1School of Computer and Information Engineering, Xiamen University of Technology, Xiamen 361024, China.

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|July 29, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a Bayesian quantile regression model for spatial data, enhancing performance predictions in smart cities. The novel approach improves decision-making by accurately capturing complex covariate effects across different data quantiles.

Keywords:
Gibbs samplingMarkov chain Monte Carlo approachpartially linear varying coefficientquantile regressionspatial autoregressive models

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Area of Science:

  • Spatial statistics
  • Econometrics
  • Urban analytics

Background:

  • Smart cities rely on spatial data for informed decision-making.
  • Existing models may not fully capture complex spatial relationships and performance variations.

Purpose of the Study:

  • To develop an advanced statistical model for improved spatial data analysis.
  • To enhance performance prediction in smart city applications using Bayesian quantile regression.
  • To capture both linear and nonlinear effects of covariates at various quantiles.

Main Methods:

  • Application of a Bayesian quantile regression (BQR) for a partially linear varying coefficient spatial autoregressive (PLVCSAR) model.
  • Approximation of nonparametric functions using free-knot splines.
  • Development of a Bayesian sampling approach via Markov chain Monte Carlo (MCMC), including an efficient Metropolis-Hastings within Gibbs algorithm.
  • Implementation of a modified reversible-jump MCMC algorithm for computational efficiency.

Main Results:

  • The proposed BQR-PLVCSAR model demonstrates robustness to different spatial weight matrices.
  • The model outperforms traditional quantile regression (QR) and instrumental variable quantile regression (IVQR) in finite sample simulations.
  • Accurate prediction of performance across various quantiles is achieved.

Conclusions:

  • The developed Bayesian quantile regression model offers a significant advancement for spatial data analysis.
  • The method provides a robust and efficient tool for improving performance predictions in smart city contexts.
  • The model's effectiveness is validated using real-world Boston housing price data.