Spatial Statistics最新文献

英文中文

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 : 2025-02-06 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

Spatial deep convolutional neural networks 空间深度卷积神经网络

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-02-06 DOI: 10.1016/j.spasta.2025.100883

Qi Wang, Paul A. Parker, Robert Lund

Spatial prediction problems often use Gaussian process models, which can be computationally burdensome in high dimensions. Specification of an appropriate covariance function for the model can be challenging when complex non-stationarities exist. Recent work has shown that pre-computed spatial basis functions and a feed-forward neural network can capture complex spatial dependence structures while remaining computationally efficient. This paper builds on this literature by tailoring spatial basis functions for use in convolutional neural networks. Through both simulated and real data, we demonstrate that this approach yields more accurate spatial predictions than existing methods. Uncertainty quantification is also considered.

空间预测问题通常使用高斯过程模型，这在高维情况下计算量很大。当存在复杂的非平稳性时，为模型指定适当的协方差函数可能具有挑战性。最近的研究表明，预先计算的空间基函数和前馈神经网络可以捕获复杂的空间依赖结构，同时保持计算效率。本文在此文献的基础上，通过裁剪空间基函数用于卷积神经网络。通过模拟和实际数据，我们证明该方法比现有方法产生更准确的空间预测。还考虑了不确定度的量化。

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 : 2025-01-27 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

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 : 2025-01-13 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

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 : 2025-01-10 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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引用次数: 0

Bias-corrected instrumental variable estimation for spatial autoregressive models with measurement errors 带有测量误差的空间自回归模型的偏差校正工具变量估计

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-12-27 DOI: 10.1016/j.spasta.2024.100878

Guowang Luo , Mixia Wu

In this paper, bias-corrected instrumental variable estimation methods, specifically the bias-corrected two-stage least square (2SLS) estimation and the bias-corrected asymptotically best 2SLS estimation, are proposed for spatial autoregressive (SAR) models with covariate measurement errors, utilizing available information regarding the variance of the measurement error. Under mild assumptions, the consistency and asymptotic normality of the proposed estimators are derived. Simulation studies further reveal that the proposed methods exhibit robustness regardless of the presence of spatial dependence in the model. Additionally, a real data example is utilized to illustrate the developed methods.

本文利用有关测量误差方差的可用信息，针对具有协变量测量误差的空间自回归（SAR）模型，提出了偏差校正的工具变量估计方法，特别是偏差校正的两阶段最小二乘（2SLS）估计和偏差校正的渐近最佳2SLS估计。在温和的假设条件下，得到了所提估计量的相合性和渐近正态性。仿真研究进一步表明，无论模型中是否存在空间依赖性，所提出的方法都具有鲁棒性。此外，还利用一个实际的数据实例来说明所开发的方法。

引用次数: 0

An optimised rabies vaccination schedule for rural settlements 优化农村居民点狂犬病疫苗接种计划

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-12-17 DOI: 10.1016/j.spasta.2024.100877

Rian Botes , Inger Fabris-Rotelli , Kabelo Mahloromela , Ding-Geng Chen

The timely and efficient administration of rabies vaccinations to animals in rural villages is necessary to attain a state of herd immunity. Efficient sampling of households in a rural village is of utmost importance in reaching the most animals for vaccination, with the least effort, and in the lowest time. This research seeks to both optimise the spatial sampling scheme used to sample households, as well as the route travelled by persons performing door-to-door vaccinations. The walking time in minutes is regarded as the cost of a vaccination scheme and is minimised in this paper. The distribution of houses in a rural village constitutes a spatial point pattern in

R^{2}

, and as such, spatial point pattern analysis techniques as well as some spatial sampling schemes are applied throughout this research. The penultimate aim of this work is to provide policy makers with additional tools to combat rabies, a disease which remains endemic to some countries in West and Central Africa, and Asia.

及时和有效地对农村动物进行狂犬病疫苗接种是实现群体免疫状态所必需的。对农村家庭进行有效抽样对于以最少的努力和最短的时间为最多的动物接种疫苗至关重要。本研究旨在优化用于对家庭进行抽样的空间抽样方案，以及进行挨家挨户接种疫苗的人员所经过的路线。以分钟为单位的步行时间被视为疫苗接种方案的成本，并在本文中最小化。乡村房屋的分布构成了R2中的空间点格局，因此在本研究中采用了空间点格局分析技术和一些空间采样方案。这项工作的第二个目标是为决策者提供防治狂犬病的额外工具，这种疾病在西非和中非以及亚洲的一些国家仍然流行。

引用次数: 0

Softening the criteria for determining inner and outer predicted exceedance sets 软化确定内部和外部预测超出集的标准

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-12-17 DOI: 10.1016/j.spasta.2024.100876

Thomas Suesse , Alexander Brenning

Determining exceedance regions, such as regions where a specified threshold of a pollutant in the environment is exceeded, is of critical importance for decision-making in environmental management and public health. Inner and outer predicted exceedance sets express the uncertainties in predicted exceedance regions as they sandwich the unknown true exceedance region with high confidence, analogous to confidence regions for point estimates. It is therefore desirable to reduce the uncertainty about the locations of the true exceedance region, resulting in a narrow band between the inner and outer sets. However, in practice this is not often the case mainly due to the strict statistical subset criteria being set, which are equivalent to a multiple testing problem controlling the familywise error rate (FWER). It is well known that the FWER leads to fewer rejections compared to other criteria; in the context of exceedance regions, this would correspond to an extremely small, conservative inner predicted exceedance region. In this paper, we loosen the criteria slightly to obtain a narrower band between inner and outer sets, allowing for more nuanced uncertainty assessments. A new algorithm is proposed to construct these exceedance sets, and the methods are compared in a simulation study to assess whether they indeed control the new criteria. The methods are illustrated on two data sets: average rainfall in the state of Paraná, Brazil, and nitrogen dioxide air pollution in Germany in the year 2018.

确定超标区域，例如环境中污染物超过规定阈值的区域，对环境管理和公共卫生决策至关重要。内部和外部预测超越集表示预测超越区域的不确定性，因为它们以高置信度夹在未知的真实超越区域中，类似于点估计的置信度区域。因此，需要减少真实超出区域位置的不确定性，从而使内外集之间的频带变窄。然而，在实践中，这种情况并不常见，主要是由于设置了严格的统计子集标准，这相当于控制家庭错误率（FWER）的多个测试问题。众所周知，与其他标准相比，FWER会导致更少的拒绝；在超出区域的情况下，这将对应于一个极小的、保守的内部预测超出区域。在本文中，我们稍微放宽了标准，以在内外集之间获得更窄的频带，从而允许更细微的不确定性评估。提出了一种新的算法来构造这些超越集，并在仿真研究中比较了各种方法，以评估它们是否确实控制了新的准则。这些方法在两个数据集上得到了说明：巴西帕拉纳州的平均降雨量和德国2018年的二氧化氮空气污染。

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引用次数: 0

Fixed effects spatial panel interval-valued autoregressive models and applications 固定效应空间面板区间值自回归模型及其应用

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-11-26 DOI: 10.1016/j.spasta.2024.100875

Qingqing Li, Ruizhuo Zheng, Aibing Ji, Hongyan Ma

Interval-valued data has garnered attention across various applications, leading to increased research into spatial interval-valued data models. The integration of uncertainty variables into spatial panel data models has become crucial. This paper presents a spatial panel interval-valued autoregressive model with fixed effects, utilizing the parametric method. The quasi-maximum likelihood method is employed for parameter estimation, and its consistency and asymptotic properties are discussed. Additionally, three special cases and two degenerated models derived from our framework are presented, elucidating their significance in spatial statistics. Monte Carlo simulations are used to validate the fitting and forecasting performance of our proposed models across diverse scenarios. Furthermore, the models are implemented in real-world air quality and house price datasets for forecasting purposes. Through rigorous experimentation, the superior performance of the models is demonstrated. These results highlight the practical utility of the spatial panel interval-valued autoregressive models in addressing spatial data challenges.

区间值数据在各种应用中引起了人们的关注，导致对空间区间值数据模型的研究增加。将不确定性变量整合到空间面板数据模型中变得至关重要。本文利用参数化方法建立了具有固定效应的空间面板区间值自回归模型。采用拟极大似然方法进行参数估计，讨论了拟极大似然方法的相合性和渐近性。此外，本文还提出了三个特例和两个退化模型，阐明了它们在空间统计中的意义。蒙特卡罗模拟用于验证我们提出的模型在不同情景下的拟合和预测性能。此外，这些模型在现实世界的空气质量和房价数据集中实施，用于预测目的。通过严格的实验，证明了模型的优越性能。这些结果突出了空间面板区间值自回归模型在解决空间数据挑战方面的实际效用。

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引用次数: 0

Fuzzy clustering of mixed data with spatial regularization 利用空间正则化对混合数据进行模糊聚类

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-11-23 DOI: 10.1016/j.spasta.2024.100874

Pierpaolo D’Urso , Livia De Giovanni , Lorenzo Federico , Vincenzina Vitale

A fuzzy clustering model for data with mixed features and spatial constraints is proposed. The clustering model allows different types of variables, or attributes, to be taken into account. This result is achieved by combining the dissimilarity measures for each attribute employing a weighting scheme, to obtain a distance measure for multiple attributes. The weights are objectively computed during the optimization process. The weights reflect the relevance of each attribute type in the clustering results. A spatial term is taken into account, considering a wide definition of contiguity, either physical contiguity or the adjacency matrix in a network. Simulation studies and two empirical applications, including both physical and abstract definitions of contiguity are presented that show the effectiveness of the proposed clustering model.

本文提出了一种针对具有混合特征和空间限制的数据的模糊聚类模型。该聚类模型允许考虑不同类型的变量或属性。这一结果是通过采用加权方案将每个属性的不相似度量结合起来，从而获得多个属性的距离度量。权重是在优化过程中客观计算出来的。权重反映了每种属性类型在聚类结果中的相关性。考虑到连续性的广泛定义，即物理连续性或网络中的邻接矩阵，空间项也被考虑在内。模拟研究和两个经验应用（包括物理和抽象定义的毗连性）显示了建议聚类模型的有效性。

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全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

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Spatial Statistics

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