复杂约束域上变系数融合空间点过程强度估计
Fused Spatial Point Process Intensity Estimation with Varying Coefficients on Complex Constrained Domains
摘要：
在精确位置进行地理编码的大型空间数据的可用性，推动了对点过程的空间建模和分析的兴趣日益增长。所提出的研究的动机是$\mathbb{R}^2$中复杂域上的大空间点图案的强度估计问题（例如，由于地理约束而具有不规则边界、尖锐凹陷和/或内部孔洞的域）和线性网络，其中许多现有的空间点过程模型遭受“泄漏”和计算的问题。我们提出了一个有效的强度估计算法来估计空间变化的强度函数，并研究强度和解释变量之间的变化关系。该方法是建立在一个图形正则化技术，因此可以灵活地应用于点模式的复杂域，如不规则的边界和洞，或线性网络的区域。提出了一种有效的邻近梯度优化算法来处理大空间点模式。我们还推导出所提出的估计的渐近误差界。数值研究来说明该方法的性能。最后，我们应用该方法来研究和可视化的强度模式的事故在西澳大利亚州的道路网络，和空间变化的影响，收入，照明条件，和人口密度对多伦多凶杀案的发生。
英文摘要：
The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large spatial point patterns on complex domains in $\mathbb{R}^2$ (e.g., domains with irregular boundaries, sharp concavities, and/or interior holes due to geographic constraints) and linear networks, where many existing spatial point process models suffer from the problems of "leakage" and computation. We propose an efficient intensity estimation algorithm to estimate the spatially varying intensity function and to study the varying relationship between intensity and explanatory variables on complex domains. The method is built upon a graph regularization technique and hence can be flexibly applied to point patterns on complex domains such as regions with irregular boundaries and holes, or linear networks. An efficient proximal gradient optimization algorithm is proposed to handle large spatial point patterns. We also derive the asymptotic error bound for the proposed estimator. Numerical studies are conducted to illustrate the performance of the method. Finally, we apply the method to study and visualize the intensity patterns of the accidents on the Western Australia road network, and the spatial variations in the effects of income, lights condition, and population density on the Toronto homicides occurrences.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
