Spatial Statistics最新文献

英文中文

Spatiotemporal mapping and analysis of atypical COVID-19 outbreaks in Shijiazhuang City (China) using the synthetic SEIR-BME approach 基于SEIR-BME方法的石家庄市非典型COVID-19疫情时空制图与分析

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-08-01 Epub Date: 2025-06-07 DOI: 10.1016/j.spasta.2025.100910

Zekun Gao , Yutong Jiang , Junjie Yin , Jiaping Wu , Maria-Stephania Christakos , George Christakos , Junyu He

Shijiazhuang City (Hebei Province, China) experienced two COVID-19 outbreaks: January 2021 and November 2022. Differences in the prevention and control measures implemented during the two outbreaks led to significantly distinct epidemic evolutions. During the first outbreak, these measures were implemented throughout the epidemic duration. During the second outbreak, attention was paid only at the initial epidemic stage, followed by a laissez-faire management that led to a rapid epidemic development, and only then control measures were re-implemented. In the present work, epidemic-related data during the two outbreaks and relevant risk area data during the atypical November 2022 outbreak were collected from Nation-, Hebei Province-, and Shijiazhuang City-level Health Commission sources. The study of the outbreaks involved a preliminary long time-series analysis followed by a novel synthesis of Susceptible-Exposed-Infected-Removed (SEIR) modeling with Bayesian Maximum Entropy (BME) mapping of the spatiotemporal COVID-19 spread during the November 2022 outbreak (a severe data deficiency occurred this month due to normalized management). An important advantage of the proposed SEIR-BME synthesis is that it compensated for the individual shortcomings of its components: Using SEIR we constructed transmission models of the outbreaks, while BME effectively filled in the missing data during November 2022 and subsequently generated accurate spatiotemporal disease risk maps. Our results confirmed the powerful transmission capability of COVID-19 and the considerable prevention and control progress made by the authorities from January 2021 to November 2022. We also found that during the exponential growth period of the epidemic, the COVID-19 variation results of this work closely followed the empirical COVID-19 law of He et al. (2020). Lastly, our analysis provided data support for subsequent studies of the COVID-19 spread, and suggested optimal infectious disease prevention and control measures. It is hoped that the present work would laid the methodological foundations for future developments in spatiotemporal infectious disease modeling and mapping.

中国河北省石家庄市经历了两次COVID-19疫情：2021年1月和2022年11月。在两次疫情期间实施的预防和控制措施的差异导致了明显不同的流行病演变。在第一次疫情期间，这些措施在整个疫情期间都得到了实施。在第二次暴发期间，只注意了最初的流行阶段，随后采取了放任管理，导致流行病迅速发展，直到那时才重新实施控制措施。在本工作中，从国家、河北省和石家庄市卫生委员会收集了两次疫情期间的流行病学相关数据和2022年11月非典型疫情期间的相关风险区域数据。对疫情的研究包括初步的长时间序列分析，然后对2022年11月疫情期间COVID-19时空传播的贝叶斯最大熵（BME）映射进行易感-暴露-感染-去除（SEIR）模型的新颖综合（由于规范化管理，本月发生了严重的数据不足）。提出的SEIR-BME综合的一个重要优势是它弥补了其组成部分的单个缺点：使用SEIR，我们构建了疫情的传播模型，而BME有效地填补了2022年11月期间缺失的数据，随后生成了准确的时空疾病风险图。我们的结果证实了2019冠状病毒病的强大传播能力，以及当局在2021年1月至2022年11月期间取得的相当大的防控进展。我们还发现，在疫情的指数增长期，本工作的COVID-19变异结果与He et al.（2020）的经验COVID-19规律密切相关。最后，我们的分析为后续的COVID-19传播研究提供了数据支持，并提出了最佳的传染病防控措施。希望本研究能为传染病时空建模和制图的未来发展奠定方法学基础。

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引用次数: 0

Probabilistic spatiotemporal modeling of day-ahead wind power generation with input-warped Gaussian processes 基于输入扭曲高斯过程的日前风力发电概率时空建模

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-08-01 Epub Date: 2025-06-01 DOI: 10.1016/j.spasta.2025.100906

Qiqi Li , Michael Ludkovski

We design a Gaussian process (GP) spatiotemporal model to capture features of day-ahead wind power forecasts. We work with hourly-scale day-ahead forecasts across hundreds of wind farm locations, with the main aim of constructing a fully probabilistic joint model across space and hours of the day. To this end, we design a separable space–time kernel, implementing both temporal and spatial input warping to capture the nonstationarity in the covariance of wind power. We conduct synthetic experiments to validate our choice of the spatial kernel and to demonstrate the effectiveness of warping in addressing nonstationarity. The second half of the paper is devoted to a detailed case study using a realistic, fully calibrated dataset representing wind farms in the ERCOT region of Texas.

我们设计了一个高斯过程（GP）时空模型来捕捉日前风电预测的特征。我们在数百个风电场的位置上进行小时尺度的前一天预测，主要目的是建立一个跨空间和一天中的小时的全概率联合模型。为此，我们设计了一个可分离的时空核，实现了时间和空间的输入扭曲，以捕获风电协方差的非平稳性。我们进行了综合实验来验证我们对空间核的选择，并证明了翘曲在解决非平稳性方面的有效性。本文的后半部分是一个详细的案例研究，使用了一个真实的、完全校准的数据集，代表了德克萨斯州ERCOT地区的风力发电场。

引用次数: 0

Bias correction methods for spatially lagged covariates measured with errors 带有误差测量的空间滞后协变量的偏差校正方法

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-08-01 Epub Date: 2025-05-29 DOI: 10.1016/j.spasta.2025.100909

Mohammad Masjkur , Asep Saefuddin , I. Wayan Mangku , Henk Folmer , Arno J. Van der Vlist , Marco Grzegorczyk

This paper compares three widely applied bias correction methods for spatially lagged covariates measured with error, namely, Monte Carlo expectation-maximization (MCEM), instrumental variables (IV), and Bayesian analysis (BA). We cross-compare these correction methods on simulated data for the special case of one single lagged covariate. We use the root mean squared error (RMSE) as evaluation criterion. The findings indicate that BA is the best bias correction method.

本文比较了蒙特卡罗期望最大化法（MCEM）、工具变量法（IV）和贝叶斯分析法（BA）三种应用广泛的空间滞后协变量偏差校正方法。对于单一滞后协变量的特殊情况，我们在模拟数据上对这些校正方法进行了交叉比较。我们使用均方根误差（RMSE）作为评价标准。结果表明，BA是最好的偏置校正方法。

引用次数: 0

Transfer learning for high dimensional spatial autoregressive model 高维空间自回归模型的迁移学习

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-08-01 Epub Date: 2025-06-13 DOI: 10.1016/j.spasta.2025.100908

Yunquan Song, Xuan Chen, Rui Yang, Yijun Li

Transfer learning is a learning process that applies models learned in old domains to new domains by utilizing similarities between data, tasks, or models. At present, transfer learning has been widely applied, such as natural language processing, recommendation systems, drug analysis, etc. Research in statistical models mostly focuses on classic linear models such as classification and regression. It is still unclear how transfer learning affects spatial data. Spatial data is an important type of data and has been a hot research topic in statistics and econometrics in recent years. However, in reality, its collection and labeling are expensive and labor-intensive, and there may not be enough data to train a robust model. Therefore, this article considers using auxiliary sample sets that are different from the target dataset but have some similarity to help us estimate and predict the target model, and specifies criteria for determining similarity. We propose transfer learning algorithms based on spatial autoregressive models, which can transfer knowledge from auxiliary datasets to target models of interest to us. Its performance has been demonstrated in numerical simulations and real housing price datasets.

迁移学习是一种学习过程，通过利用数据、任务或模型之间的相似性，将在旧领域学习到的模型应用到新领域。目前，迁移学习已经得到了广泛的应用，如自然语言处理、推荐系统、药物分析等。统计模型的研究主要集中在分类、回归等经典线性模型上。目前尚不清楚迁移学习如何影响空间数据。空间数据是一种重要的数据类型，是近年来统计学和计量经济学研究的热点。然而，在现实中，它的收集和标记是昂贵和劳动密集型的，并且可能没有足够的数据来训练一个鲁棒模型。因此，本文考虑使用与目标数据集不同但具有一定相似性的辅助样本集来帮助我们估计和预测目标模型，并规定了确定相似性的标准。我们提出了基于空间自回归模型的迁移学习算法，该算法可以将知识从辅助数据集转移到我们感兴趣的目标模型。通过数值模拟和实际房价数据集验证了其性能。

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引用次数: 0

A marked sequential point process for disease surveillance: Modeling and optimization 疾病监测的标记顺序点过程：建模与优化

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-08-01 Epub Date: 2025-06-28 DOI: 10.1016/j.spasta.2025.100913

François d’Alayer, Edith Gabriel, Samuel Soubeyrand

Plant disease surveillance is essential for the management of disease outbreaks that pose significant threats to agricultural sustainability. In this study, we present a novel sequential point process model designed for disease surveillance. The model incorporates self-interaction mechanisms to account for the influence of the process’ history. To analyze the dynamics of the model, we propose new sequential summary statistics that extend traditional point process methods to scenarios where sequential interactions are critical. This model serves a dual purpose: it is employed both to propose novel and efficient sampling designs, and to characterize existing sampling schemes, implemented in real-world situations, through parameter inference.

植物病害监测对于管理对农业可持续性构成重大威胁的病害暴发至关重要。在这项研究中，我们提出了一种新的序列点过程模型，用于疾病监测。该模型结合了自交互机制来解释过程历史的影响。为了分析模型的动态，我们提出了新的顺序汇总统计，将传统的点处理方法扩展到顺序交互至关重要的场景。该模型具有双重目的：既可以提出新颖有效的抽样设计，又可以通过参数推理来表征在现实世界中实施的现有抽样方案。

引用次数: 0

A low-rank Bayesian approach for geoadditive modeling geoadditive建模的低秩贝叶斯方法

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-08-01 Epub Date: 2025-06-03 DOI: 10.1016/j.spasta.2025.100907

Bryan Sumalinab , Oswaldo Gressani , Niel Hens , Christel Faes

Kriging is an established methodology for predicting spatial data in geostatistics. Current kriging techniques can handle linear dependencies on spatially referenced covariates. Although splines have shown promise in capturing nonlinear dependencies of covariates, their combination with kriging, especially in handling count data, remains underexplored. This paper proposes a new Bayesian approach to the low-rank representation of geoadditive models, which integrates splines and kriging to account for both spatial correlations and nonlinear dependencies of covariates. The proposed method accommodates Gaussian and count data inherent in many geospatial datasets. Additionally, Laplace approximations to selected posterior distributions enhances computational efficiency, resulting in faster computation times compared to Markov chain Monte Carlo techniques commonly used for Bayesian inference. Method performance is assessed through a simulation study, demonstrating the effectiveness of the proposed approach. The methodology is applied to the analysis of heavy metal concentrations in the Meuse river and vulnerability to the coronavirus disease 2019 (COVID-19) in Belgium.

克里格是地质统计学中预测空间数据的常用方法。当前的克里格技术可以处理空间引用协变量的线性依赖关系。尽管样条在捕获协变量的非线性依赖关系方面显示出了希望，但它们与克里格的结合，特别是在处理计数数据方面，仍未得到充分的探索。本文提出了一种新的贝叶斯方法来处理geoadditive模型的低秩表示，该方法将样条和kriging相结合，以考虑协变量的空间相关性和非线性依赖性。该方法可以适应许多地理空间数据集中固有的高斯和计数数据。此外，选择后验分布的拉普拉斯近似提高了计算效率，与贝叶斯推理常用的马尔可夫链蒙特卡罗技术相比，计算时间更快。通过仿真研究对方法性能进行了评估，验证了所提方法的有效性。该方法应用于分析比利时默兹河重金属浓度和对2019冠状病毒病（COVID-19）的易感性。

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引用次数: 0

Characteristics of some isotropic covariance models with negative values 负各向同性协方差模型的特征

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-08-01 Epub Date: 2025-06-08 DOI: 10.1016/j.spasta.2025.100905

De Iaco S., Posa D.

In the literature, most of the classical covariance models characterised by negative values were derived by utilising the Bessel functions, on the other hand, recently, other classes of models with negative correlation were obtained through the difference between two covariance functions. However, although for the former, the analytic features, such as their absolute minimum values, were completely explored, for the latter these aspects have to be still investigated. In this paper, starting from the admissibility conditions and the general characteristics of three wide families of isotropic covariance models, based on the difference of Gaussian, exponential and rational models, their absolute minimum, as a function of the dimension of the Euclidean space in which they are defined, is provided. Consequently, the minimum values for the most common Euclidean dimensional spaces are given as special cases. These results fill the theoretical gap related to the analysed classes of correlation models with negative values and then can support their use. A simulation study and an application to a real data set are also presented to assess performance in terms of prediction accuracy.

在文献中，大多数以负值为特征的经典协方差模型都是利用贝塞尔函数推导出来的，另一方面，近年来，通过两个协方差函数的差来获得其他类型的负相关模型。然而，虽然对于前者，分析特征，如它们的绝对最小值，已经被完全探索，对于后者，这些方面仍然需要研究。本文从三大类各向同性协方差模型的容错条件和一般特征出发，基于高斯模型、指数模型和有理模型的差异，给出了它们的绝对极小值作为它们所定义的欧几里得空间维数的函数。因此，对于最常见的欧几里得维空间的最小值作为特殊情况给出。这些结果填补了与所分析的具有负值的相关模型类别相关的理论空白，从而可以支持它们的使用。通过仿真研究和对真实数据集的应用来评估预测精度方面的性能。

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引用次数: 0

Magnitude-weighted goodness-of-fit scores for earthquake forecasting 地震预报的震级加权拟合优度分数

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-06-01 Epub Date: 2025-03-28 DOI: 10.1016/j.spasta.2025.100895

Frederic Schoenberg

Current methods for evaluating earthquake forecasts, such as the

N

-test,

L

-test, or log-likelihood score, typically do not disproportionately reward a model for more accurately forecasting the largest events, or disproportionately punish a model for less accurately forecasting the largest events. However, since the largest earthquakes are by far the most destructive and therefore of most interest to practitioners, in many circumstances, a weighted likelihood score may be more useful. Here, we propose various weighted measures, weighting each earthquake by some function of its magnitude, such as potency-weighted log-likelihood, and consider their properties. The proposed methods are applied to a catalog of earthquakes in the Western United States.

目前评估地震预报的方法，如n检验、l检验或对数似然评分，通常不会不成比例地奖励更准确预测最大事件的模型，或者不成比例地惩罚预测最大事件不准确的模型。然而，由于最大的地震是迄今为止最具破坏性的，因此从业人员最感兴趣，在许多情况下，加权可能性评分可能更有用。在这里，我们提出了各种加权措施，通过其震级的某些函数对每个地震进行加权，例如势加权对数似然，并考虑它们的性质。所提出的方法应用于美国西部的地震目录。

引用次数: 0

A new regular grid-based spatial process on the log-symmetric model for speckled clutter 基于对数对称模型的斑点杂波规则网格空间处理方法

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.2025.100900

Arthur Machado, Francisco José A. Cysneiros, Abraão D.C. Nascimento

Solving remote sensing (RS) problems is crucial for society when it comes to environmental and climate dynamics, to name just a few examples. An efficient RS source is the use of synthetic aperture radar (SAR) to describe natural and man-made phenomena through imagery. Our approach is to understand the data behind SAR images as outcomes of random variables, and then use statistics to solve RS problems. In this paper, we consider the input of a SAR image as a random variable in regular space and describe the nature of SAR intensity (a strictly positive and asymmetric feature that is affected by speckle noise and prevents direct interpretation) using a new proposal for a log-symmetric (LOGSYM) regression model in two dimensions, the 2-D LOGSYM autoregressive moving-average (2-D LOGSYMARMA) model. Besides a discussion on the physical relationship between the proposed model and SAR intensity (mentioning that it can extend a commonly used lognormal law), we derive some mathematical properties of 2-D LOGSYMARMA: matrix-based score function and Fisher information. We discuss in detail the conditional maximum likelihood (CML) estimation for the 2-D LOGSYMARMA parameters. We conduct a Monte Carlo study to quantify the performance of the resulting estimates and to verify that the asymptotic behavior expected from CML estimators is achieved. Finally, we perform an application to real SAR data, where our proposal is applied to different types of regions – ocean, forest, and urban areas – utilizing the versatility of the log-symmetric family. Results of both artificial and real experiments show that our model is an important tool for the extraction and classification of spatial information in SAR images.

在环境和气候动力学方面，解决遥感（RS）问题对社会至关重要，仅举几个例子。一种有效的遥感源是利用合成孔径雷达（SAR）通过图像描述自然和人为现象。我们的方法是将SAR图像背后的数据理解为随机变量的结果，然后使用统计学来解决RS问题。在本文中，我们将SAR图像的输入视为正则空间中的随机变量，并使用二维LOGSYM自回归移动平均（2d LOGSYMARMA）模型的新提议来描述SAR强度的性质（受散斑噪声影响并阻止直接解释的严格正非对称特征）。除了讨论所提出的模型与SAR强度之间的物理关系（提到它可以扩展常用的对数正态律）外，我们还推导了二维LOGSYMARMA的一些数学性质：基于矩阵的分数函数和Fisher信息。详细讨论了二维LOGSYMARMA参数的条件最大似然估计（CML）。我们进行了蒙特卡罗研究，以量化结果估计的性能，并验证了CML估计器所期望的渐近行为是实现的。最后，我们对真实的SAR数据进行了应用，其中我们的建议应用于不同类型的区域-海洋，森林和城市地区-利用对数对称族的多功能性。人工实验和实际实验结果表明，该模型是SAR图像空间信息提取和分类的重要工具。

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引用次数: 0

A spatial autoregressive graphical model 空间自回归图形模型

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-06-01 Epub Date: 2025-04-15 DOI: 10.1016/j.spasta.2025.100893

Sjoerd Hermes , Joost van Heerwaarden , Pariya Behrouzi

Within the statistical literature, a significant gap exists in methods capable of modelling asymmetric multivariate spatial effects that elucidate the relationships underlying complex spatial phenomena. For such a phenomenon, observations at any location are expected to arise from a combination of within- and between-location effects, where the latter exhibit asymmetry. This asymmetry is represented by heterogeneous spatial effects between locations pertaining to two different categories, that is, a feature inherent to each location in the data, such that based on the feature label, asymmetric spatial relations are postulated between neighbouring locations with different labels. Our novel approach synergises the principles of multivariate spatial autoregressive models and the Gaussian graphical model. This synergy enables us to effectively address the gap by accommodating asymmetric spatial relations, overcoming the usual constraints in spatial analyses. However, the resulting flexibility comes at a cost: the spatial effects are not identifiable without either prior knowledge of the underlying phenomenon or additional parameter restrictions. Using a Bayesian-estimation framework, the model performance is assessed in a simulation study. We apply the model on intercropping data, where spatial effects between different crops are unlikely to be symmetric, in order to illustrate the usage of the proposed methodology. An R package containing the proposed methodology can be found on https://CRAN.R-project.org/package=SAGM.

在统计文献中，在能够模拟非对称多元空间效应的方法上存在着显著的差距，这些方法阐明了复杂空间现象背后的关系。对于这种现象，任何位置的观测结果都可能是由位置内效应和位置间效应的组合引起的，其中后者表现出不对称性。这种不对称表现为属于两个不同类别的位置之间的异构空间效应，即数据中每个位置固有的特征，因此基于特征标签，假设具有不同标签的相邻位置之间存在不对称空间关系。我们的新方法协同多元空间自回归模型和高斯图形模型的原理。这种协同作用使我们能够通过适应不对称的空间关系来有效地解决差距，克服空间分析中的通常限制。然而，由此产生的灵活性是有代价的：如果没有对潜在现象或附加参数限制的先验知识，则无法识别空间效应。利用贝叶斯估计框架，对模型的性能进行了仿真研究。我们将该模型应用于间作数据，其中不同作物之间的空间效应不太可能对称，以说明所提出方法的使用。包含建议的方法的R包可以在https://CRAN.R-project.org/package=SAGM上找到。

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