Spatial Statistics最新文献

英文中文

Integrating multi-source geospatial information using Bayesian maximum entropy: A case study on design ground snow load prediction 基于贝叶斯最大熵的多源地理空间信息集成——以设计地面雪荷载预测为例

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-06-01 Epub Date: 2025-03-26 DOI: 10.1016/j.spasta.2025.100894

Kinspride Duah, Yan Sun, Brennan Bean

Environmental data are often imprecise due to various limitations and uncertainties in the measuring process. As a result, they often consist of a combination of both precise and imprecise information, referred to as hard and soft data, respectively. Often in practice, soft data are characterized as intervals as a simple form to properly preserve the underlying imprecision. Bayesian maximum entropy (BME) is a generalized spatial interpolation method that processes both hard and soft data simultaneously to effectively account for both spatial uncertainty and measurement imprecision. This paper presents a rigorous evaluation to compare the performances of BME and kriging through both simulation and a case study of reliability-targeted design ground snow load (RTDSL) prediction in Utah. The dataset contains a mixture of hard and soft-interval observations, and kriging uses the soft-interval data by extracting the midpoints in addition to the hard data. The cross-validated results show that BME outperforms kriging on multiple error metrics. Specifically for hard data locations where precise observations are known, BME yields a mean error (ME) of 0.0334, a mean absolute error (MAE) of 0.2309, and a root mean squared error (RMSE) of 0.2833, whereas kriging produces a ME of 0.1960, MAE of 0.2793, and RMSE of 0.3698. These results highlight the superior prediction accuracy of BME, particularly in the presence of soft data and/or non-Gaussian hard data.

由于测量过程中的各种限制和不确定性，环境数据往往是不精确的。因此，它们通常由精确和不精确信息的组合组成，分别称为硬数据和软数据。通常在实践中，软数据被描述为间隔，作为一种简单的形式，以适当地保留潜在的不精确性。贝叶斯最大熵（BME）是一种广义的空间插值方法，它同时处理硬数据和软数据，以有效地解释空间不确定性和测量不精度。本文通过仿真和可靠性目标设计地面雪荷载（RTDSL）预测的实例研究，对BME和kriging的性能进行了严格的评价。该数据集包含硬间隔和软间隔观测数据的混合，kriging通过在硬数据之外提取中点来使用软间隔数据。交叉验证结果表明，BME算法在多个误差指标上优于克里格算法。特别是对于已知精确观测值的硬数据位置，BME产生的平均误差（ME）为0.0334，平均绝对误差（MAE）为0.2309，均方根误差（RMSE）为0.2833，而克里格产生的ME为0.1960，MAE为0.2793，RMSE为0.3698。这些结果突出了BME的优越预测精度，特别是在软数据和/或非高斯硬数据的存在下。

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引用次数: 0

Functional summary statistics and testing for independence in multi-type point processes on the surface of three dimensional convex shapes 三维凸形表面多类型点加工的功能汇总统计与独立性检验

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-06-01 Epub Date: 2025-03-13 DOI: 10.1016/j.spasta.2025.100891

S. Ward, E.A.K. Cohen, N.M. Adams

The fundamental functional summary statistics used for studying spatial point patterns are developed for marked homogeneous and inhomogeneous point processes on the surface of a sphere. These are extended to point processes on the surface of three dimensional convex shapes given the bijective mapping from the shape to the sphere is known. These functional summary statistics are used to test for independence between the marginals of multi-type spatial point processes with methods for sampling the null distribution developed and discussed. This is illustrated on both simulated data and the RNGC galaxy point pattern, revealing attractive dependencies between different galaxy types.

针对球面上有标记的齐次和非齐次点过程，建立了用于空间点模式研究的基本功能汇总统计量。这些扩展到三维凸形状表面上的点过程，给定从形状到球体的双射映射是已知的。这些功能汇总统计数据用于检验多类型空间点过程的边缘之间的独立性，并开发和讨论了对零分布进行抽样的方法。模拟数据和RNGC星系点图都说明了这一点，揭示了不同星系类型之间的吸引力依赖关系。

引用次数: 0

Stochastic spatial stream networks for scalable inferences of riverscape processes 用于河流景观过程可扩展推理的随机空间流网络

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-06-01 Epub Date: 2025-04-25 DOI: 10.1016/j.spasta.2025.100902

Xinyi Lu , Andee Kaplan , Yoichiro Kanno , George Valentine , Jacob M. Rash , Mevin Hooten

Spatial stream networks (SSN) models characterize correlated ecological processes in dendritic ecosystems. Conventional SSN models rely on pre-processed stream networks and point-to-point hydrologic distances. However, this data processing may be labor-intensive and time-consuming over large spatial domains. Therefore, we propose to infer the functional connectivity of stream networks stochastically. Our physically-guided model utilizes the knowledge that water flows from high elevation to low elevation, and flow rate typically increases when two tributaries merge. We also leverage the hierarchical branching architecture of dendritic networks to alleviate computing and reduce uncertainty. Spatial autoregressive models composed of inferred SSNs propagate stochasticity between network connectivity and dynamic ecological processes in a Bayesian framework. We show in simulated examples that our mechanistic model facilitated learning about the functional network and enhanced predictive performance. We also demonstrate our approach in a large-scale case study using native brook trout (Salvelinus fontinalis) count data. A population model based on our stochastic SSN outperformed that with a conventional SSN in predicting abundance and expedited the analysis by circumventing data processing.

空间流网络（SSN）模型描述了树突生态系统的相关生态过程。传统的SSN模型依赖于预处理的河流网络和点对点的水文距离。然而，在大的空间域中，这种数据处理可能是劳动密集型和耗时的。因此，我们建议随机推断流网络的功能连通性。我们的物理导向模型利用了水从高海拔流向低海拔的知识，当两条支流合并时，流速通常会增加。我们还利用树突网络的分层分支架构来减轻计算和减少不确定性。由推断ssn组成的空间自回归模型在贝叶斯框架下传播网络连通性和动态生态过程之间的随机性。我们在模拟示例中表明，我们的机制模型促进了对功能网络的学习并增强了预测性能。我们还展示了我们的方法在一个大规模的案例研究中使用本地溪鳟（Salvelinus fontinalis）计数数据。基于随机社会安全系数的种群模型在预测丰度方面优于传统社会安全系数，并通过避免数据处理加快了分析速度。

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引用次数: 0

Clustered factor analysis for multivariate spatial data 多元空间数据的聚类因子分析

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-04-01 Epub Date: 2025-02-22 DOI: 10.1016/j.spasta.2025.100889

Yanxiu Jin , Tomoya Wakayama , Renhe Jiang , Shonosuke Sugasawa

Factor analysis has been extensively used to reveal the dependence structures among multivariate variables, offering valuable insight in various fields. However, it cannot incorporate the spatial heterogeneity that is typically present in spatial data. To address this issue, we introduce an effective method specifically designed to discover the potential dependence structures in multivariate spatial data. Our approach assumes that spatial locations can be approximately divided into a finite number of clusters, with locations within the same cluster sharing similar dependence structures. By leveraging an iterative algorithm that combines spatial clustering with factor analysis, we simultaneously detect spatial clusters and estimate a unique factor model for each cluster. The proposed method is evaluated through comprehensive simulation studies, demonstrating its flexibility. In addition, we apply the proposed method to a dataset of railway station attributes in the Tokyo metropolitan area, highlighting its practical applicability and effectiveness in uncovering complex spatial dependencies.

因子分析被广泛用于揭示多变量之间的依赖结构，在各个领域提供了有价值的见解。但是，它不能包含空间数据中通常存在的空间异质性。为了解决这个问题，我们引入了一种有效的方法来发现多元空间数据中潜在的依赖结构。我们的方法假设空间位置可以近似地划分为有限数量的集群，同一集群内的位置共享相似的依赖结构。通过利用空间聚类与因子分析相结合的迭代算法，我们同时检测空间聚类并估计每个聚类的独特因子模型。通过综合仿真研究对该方法进行了评价，证明了该方法的灵活性。此外，我们将该方法应用于东京大都市区的火车站属性数据集，突出了其在揭示复杂空间依赖关系方面的实用性和有效性。

引用次数: 0

Derivative-based spatial mediation with INLA-SPDE 基于INLA-SPDE的导数空间中介

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-04-01 Epub Date: 2025-02-24 DOI: 10.1016/j.spasta.2025.100885

Claudio Rubino , Chiara Di Maria , Antonino Abbruzzo , Gioacchino Bono , Germana Garofalo , Giacomo Milisenda , Giada Adelfio

In many applied fields, it may be of interest to evaluate mediational mechanisms occurring in spatial domains. The approaches proposed so far in the literature to address this issue deal with areal data and often consider linear models. In this paper, we propose an approach to assess mediation in the presence of geostatistical data by combining the integrated nested Laplace approximation (INLA) with a derivative-based approach for mediation analysis, which allows one to estimate indirect effects also in the case of nonlinear models. We investigate the effect of ignoring spatial processes in the mediator and the outcome models through a simulation study, focusing also on the case of correlated processes. To show the usefulness of our approach, we also provided an ecological application.

在许多应用领域中，评估空间域中发生的中介机制可能会引起人们的兴趣。到目前为止，文献中提出的解决这一问题的方法处理的是面数据，并且经常考虑线性模型。在本文中，我们提出了一种在地质统计数据存在的情况下评估中介的方法，通过将集成嵌套拉普拉斯近似（INLA）与基于导数的中介分析方法相结合，该方法允许人们在非线性模型的情况下估计间接影响。我们通过模拟研究考察了忽略中介和结果模型中空间过程的影响，并重点研究了相关过程的情况。为了展示我们方法的有效性，我们还提供了一个生态应用程序。

引用次数: 0

Clustering of compound events based on multivariate comonotonicity 基于多元共单调性的复合事件聚类

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-04-01 Epub Date: 2025-01-27 DOI: 10.1016/j.spasta.2025.100881

Fabrizio Durante , Sebastian Fuchs , Roberta Pappadà

Driven by the goal of generating risk maps for flood events—characterized by various physical variables such as peak flow and volume, and measured at specific geographic locations—this work proposes several dissimilarity functions for use in unsupervised learning problems and, specifically, in clustering algorithms. These dissimilarities are rank-based, relying on the dependence occurring among the random variables involved, and assign the smallest values to pairs of subsets that are

π

-comonotonic. This concept is less restrictive than classical comonotonicity but, in the multivariate case, can offer a more intuitive understanding of compound phenomena.

An application of these measures is presented through the analysis of flood risks using data from the Po river basin, with results compared to similar studies found in the literature.

在为洪水事件生成风险图的目标驱动下——以各种物理变量为特征，如峰值流量和体积，并在特定的地理位置进行测量——这项工作提出了几个不相似函数，用于无监督学习问题，特别是聚类算法。这些差异是基于秩的，依赖于所涉及的随机变量之间的相关性，并将最小的值分配给π共单调的子集对。这个概念比经典的共单调性限制少，但在多变量情况下，可以更直观地理解复合现象。通过使用波河流域的数据对洪水风险进行分析，提出了这些措施的应用，并将结果与文献中发现的类似研究进行了比较。

引用次数: 0

Statistical inference of partially linear time-varying coefficients spatial autoregressive panel data model 部分线性时变系数空间自回归面板数据模型的统计推断

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-04-01 Epub Date: 2025-02-18 DOI: 10.1016/j.spasta.2025.100887

Lingling Tian , Chuanhua Wei , Mixia Wu

This paper investigates a partially linear spatial autoregressive panel data model that incorporates fixed effects, constant and time-varying regression coefficients, and a time-varying spatial lag coefficient. A two-stage least squares estimation method based on profile local linear dummy variables (2SLS-PLLDV) is proposed to estimate both constant and time-varying coefficients without the need for first differencing. The asymptotic properties of the estimator are derived under certain conditions. Furthermore, a residual-based goodness-of-fit test is constructed for the model, and a residual-based bootstrap method is used to obtain p-values. Simulation studies show the good performance of the proposed method in various scenarios. For illustration, the carbon emission data from Chinese provinces and the public capital productivity data from the United States are analyzed.

本文研究了一个包含固定效应、常、时变回归系数和时变空间滞后系数的部分线性空间自回归面板数据模型。提出了一种基于剖面局部线性虚拟变量的两阶段最小二乘估计方法（2SLS-PLLDV），该方法既能估计常系数，又能估计时变系数，无需进行一次差分。在一定条件下，得到了估计量的渐近性质。在此基础上，对模型进行残差拟合优度检验，并采用残差自举法获得p值。仿真研究表明，该方法在各种场景下都具有良好的性能。本文以中国各省的碳排放数据和美国的公共资本生产率数据为例进行了分析。

引用次数: 0

Measuring unit relevance and stability in hierarchical spatio-temporal clustering 层次时空聚类中度量单元相关性和稳定性

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-04-01 Epub Date: 2025-01-13 DOI: 10.1016/j.spasta.2025.100880

Roy Cerqueti , Raffaele Mattera

Understanding the significance of individual data points within clustering structures is critical to effective data analysis. Traditional stability methods, while valuable, often overlook the nuanced impact of individual units, particularly in spatial contexts. In this paper, we explore the concept of unit relevance in clustering analysis, emphasizing its importance in capturing the spatio-temporal nature of the clustering problem. We propose a simple measure of unit relevance, the Unit Relevance Index (URI), and define an overall measure of clustering stability based on the aggregation of computed URIs. Considering two experiments on real datasets with geo-referenced time series, we find that the use of spatial constraints in the clustering task yields more stable results. Therefore, the inclusion of the spatial dimension can be seen as a way to stabilize the clustering.

理解聚类结构中单个数据点的重要性对于有效的数据分析至关重要。传统的稳定性方法虽然有价值，但往往忽略了单个单元的细微影响，特别是在空间环境中。在本文中，我们探讨了聚类分析中单位相关性的概念，强调了它在捕捉聚类问题的时空本质方面的重要性。我们提出了一种简单的单元相关性度量，即单元相关性索引（unit relevance Index， URI），并定义了基于计算的URI聚合的聚类稳定性的总体度量。通过对具有地理参考时间序列的真实数据集的两个实验，我们发现在聚类任务中使用空间约束可以获得更稳定的结果。因此，空间维度的包含可以看作是稳定聚类的一种方式。

引用次数: 0

Bayesian geographically weighted regression using Fused Lasso prior 基于融合Lasso先验的贝叶斯地理加权回归

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-04-01 Epub Date: 2025-02-06 DOI: 10.1016/j.spasta.2025.100884

Toshiki Sakai , Jun Tsuchida , Hiroshi Yadohisa

A main purpose of spatial data analysis is to predict the objective variable for the unobserved locations. Although Geographically Weighted Regression (GWR) is often used for this purpose, estimation instability proves to be an issue. To address this issue, Bayesian Geographically Weighted Regression (BGWR) has been proposed. In BGWR, by setting the same prior distribution for all locations, the coefficients’ estimation stability is improved. However, when observation locations’ density is spatially different, these methods do not sufficiently consider the similarity of coefficients among locations. Moreover, the prediction accuracy of these methods becomes worse. To solve these issues, we propose Bayesian Geographically Weighted Sparse Regression (BGWSR) that uses Bayesian Fused Lasso for the prior distribution of the BGWR coefficients. Constraining the parameters to have the same values at adjacent locations is expected to improve the prediction accuracy at locations with a low number of adjacent locations. Furthermore, from the predictive distribution, it is also possible to evaluate the uncertainty of the predicted value of the objective variable. By examining numerical studies, we confirmed that BGWSR has better prediction performance than the existing methods (GWR and BGWR) when the density of observation locations is spatial difference. Finally, the BGWSR is applied to land price data in Tokyo. Thus, the results suggest that BGWSR has better prediction performance and smaller uncertainty than existing methods.

空间数据分析的一个主要目的是预测未观测位置的客观变量。虽然地理加权回归（GWR）经常用于此目的，但估计不稳定性被证明是一个问题。为了解决这个问题，贝叶斯地理加权回归（BGWR）被提出。在BGWR中，通过对所有位置设置相同的先验分布，提高了系数估计的稳定性。然而，当观测点密度在空间上不同时，这些方法没有充分考虑到观测点间系数的相似性。而且，这些方法的预测精度变差了。为了解决这些问题，我们提出了贝叶斯地理加权稀疏回归（BGWSR），该回归使用贝叶斯融合套索进行BGWR系数的先验分布。约束参数在相邻位置具有相同的值有望提高相邻位置数量较少的位置的预测精度。此外，从预测分布中还可以评估目标变量预测值的不确定性。通过数值研究证实，当观测位置密度存在空间差异时，BGWSR的预测性能优于现有方法（GWR和BGWR）。最后，将BGWSR应用于东京地价数据。结果表明，与现有方法相比，BGWSR具有更好的预测性能和更小的不确定性。

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引用次数: 0

The Multifractal Gaussian Mixture Model for unsupervised segmentation of complex data sets 复杂数据集无监督分割的多重分形高斯混合模型

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-04-01 Epub Date: 2025-01-10 DOI: 10.1016/j.spasta.2025.100879

Garry Jacyna, Damon Frezza, David M. Slater, James R. Thompson

We derive the Multifractal Gaussian Mixture Model algorithm for decomposing data sets into different multifractal regimes building on the empirical observation that simulated multifractals have log wavelet leaders that are well-approximated by a Gaussian distribution. We test the algorithm on composite images constructed from multifractal random walks with known multifractal spectra. The algorithm is able to correctly segment the pixels corresponding to different multifractals when the constituent multifractals are most distinct from each other. It also estimates the multifractal parameters with minimal error when compared to the theoretical spectra used to generate the original multifractal random walks. We also apply the algorithm to satellite images with varying degrees of cloud cover taken from the LandSat 8 Cloud Validation Data set. The algorithm is able to segment the pixels into their corresponding cloud mask category, and it detects different texture and features in the images that are unrelated to clouds. The results indicate that the Multifractal Gaussian Mixture Model algorithm is well-suited for semi-automated unsupervised data segmentation when the data being analyzed exhibit complex, scale-invariant characteristics.

我们推导了多重分形高斯混合模型算法，用于将数据集分解为不同的多重分形制度，建立在经验观察的基础上，模拟多重分形具有由高斯分布很好地近似的对数小波前导。我们在已知多重分形谱的多重分形随机漫步合成图像上对算法进行了测试。该算法能够在组成的多重分形之间差异最大时，正确分割出不同多重分形对应的像素。与用于生成原始多重分形随机漫步的理论谱相比，它还以最小的误差估计多重分形参数。我们还将该算法应用于从LandSat 8云验证数据集中获取的不同程度云覆盖的卫星图像。该算法能够将像素分割到相应的云掩模类别中，并检测图像中与云无关的不同纹理和特征。结果表明，多重分形高斯混合模型算法非常适合于被分析数据具有复杂、尺度不变特征的半自动无监督数据分割。

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