Chen Rongshang, Chen Zhiyong
School of Computer and Information Engineering, Xiamen University of Technology, Xiamen 361024, China.
Xiamen Software Supply Chain Security Public Technology Service Platform, Xiamen 361024, China.
Entropy (Basel). 2025 Jul 1;27(7):715. doi: 10.3390/e27070715.
Spatial data not only enables smart cities to visualize, analyze, and interpret data related to location and space, but also helps departments make more informed decisions. We apply a Bayesian quantile regression (BQR) of the partially linear varying coefficient spatial autoregressive (PLVCSAR) model for spatial data to improve the prediction of performance. It can be used to capture the response of covariates to linear and nonlinear effects at different quantile points. Through an approximation of the nonparametric functions with free-knot splines, we develop a Bayesian sampling approach that can be applied by the Markov chain Monte Carlo (MCMC) approach and design an efficient Metropolis-Hastings within the Gibbs sampling algorithm to explore the joint posterior distributions. Computational efficiency is achieved through a modified reversible-jump MCMC algorithm incorporating adaptive movement steps to accelerate chain convergence. The simulation results demonstrate that our estimator exhibits robustness to alternative spatial weight matrices and outperforms both quantile regression (QR) and instrumental variable quantile regression (IVQR) in a finite sample at different quantiles. The effectiveness of the proposed model and estimation method is demonstrated by the use of real data from the Boston median house price.
空间数据不仅能使智慧城市可视化、分析和解释与位置和空间相关的数据，还能帮助各部门做出更明智的决策。我们将部分线性变系数空间自回归（PLVCSAR）模型的贝叶斯分位数回归（BQR）应用于空间数据，以改进性能预测。它可用于捕捉协变量在不同分位数点对线性和非线性效应的响应。通过使用自由节点样条对非参数函数进行近似，我们开发了一种可通过马尔可夫链蒙特卡罗（MCMC）方法应用的贝叶斯抽样方法，并在吉布斯抽样算法中设计了一种高效的梅特罗波利斯-黑斯廷斯算法来探索联合后验分布。通过结合自适应移动步骤的改进可逆跳跃MCMC算法实现计算效率，以加速链收敛。模拟结果表明，我们的估计器对替代空间权重矩阵具有稳健性，并且在不同分位数的有限样本中优于分位数回归（QR）和工具变量分位数回归（IVQR）。通过使用来自波士顿中位数房价的真实数据，证明了所提出的模型和估计方法的有效性。
