Spatial Statistics最新文献

英文中文

Nonparametric approaches for direct approximation of the spatial quantiles 直接逼近空间分位数的非参数方法

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-04-05 DOI: 10.1016/j.spasta.2025.100896

Pilar García-Soidán , Tomás R. Cotos-Yáñez

The estimation of the spatial quantiles provides information on the thresholds of a spatial variable. This methodology is particularly appealing for its application to data of pollutants, so as to assess their level of risk. A spatial quantile can be approximated through different mechanisms, proposed in the statistics literature, although these approaches suffer from several drawbacks, regarding their lack of optimality or the fact of not leading to direct approximations. Thus, the current work introduces alternative procedures, which try to overcome the aforementioned issues by employing order statistics, similarly as done for independent data. With this aim, the available observations are appropriately transformed to yield a sample of the process at each target site, so that the data obtained are then ordered and used to derive the spatial quantile at the corresponding location. The new methodology can be directly applied to data from processes that are either stationary or that deviate from this condition for a non-constant trend and, additionally, it can be even extended to heteroscedastic data. Simulation studies under different scenarios have been accomplished, whose results show the adequate performance of the proposed estimators. A further step of this research is the application of the new approaches to data of nitrogen dioxide concentrations, to exemplify the potential of the quantile estimates to check the thresholds of a pollutant at a specific moment, as well as their evolution over time.

空间分位数的估计提供了关于空间变量阈值的信息。这种方法特别有吸引力，因为它适用于污染物的数据，以便评估它们的风险水平。空间分位数可以通过统计文献中提出的不同机制进行近似，尽管这些方法存在一些缺点，例如缺乏最优性或无法直接近似。因此，目前的工作引入了替代程序，这些程序试图通过使用顺序统计来克服上述问题，类似于对独立数据所做的。为了达到这个目的，对现有的观测结果进行适当的转换，以产生每个目标地点的过程样本，以便对获得的数据进行排序，并用于推导相应位置的空间分位数。新方法可以直接应用于平稳或偏离此条件的非恒定趋势过程的数据，此外，它甚至可以扩展到异方差数据。在不同的场景下进行了仿真研究，结果表明所提出的估计器具有良好的性能。这项研究的下一步是应用二氧化氮浓度数据的新方法，以举例说明分位数估计在特定时刻检查污染物阈值的潜力，以及它们随时间的演变。

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引用次数: 0

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-03-29 DOI: 10.1016/j.spasta.2025.100897

Shifeng Yu , Xiaoyu Hu , Yehua Sheng , Chenmeng Zhao

Unlike a geographically weighted regression (GWR), a similarity and geographically weighted regression (SGWR) calculates weights using attribute and geographic similarities, thereby effectively improving the accuracy of the model. Nevertheless, SGWR does not set an attribute similarity bandwidth. This leads to its inability to measure the scale of variation of spatial processes in feature space. In addition, owing to the solving method used, SGWR can get stuck in local optima. To address these issues, this study proposed an improved similarity and geographically weighted regression model (SGWR-GD) that adds bandwidth to the attribute similarity kernel function. This parameter gives SGWR-GD the ability to measure the scale of change of spatial processes in the attribute dimension and thus enhances the flexibility of modelling. When solving the model, SGWR-GD first calculated the gradient of the model's Modified Akaike Information Criterion (AICc) with respect to the two bandwidths and the impact ratio. Subsequently, the optimal global solution of the model was obtained based on a gradient descent algorithm with box constraints. SGWR-GD and SGWR were applied to five different datasets and the accuracies of their fitting results were compared. SGWR-GD significantly improved the accuracy of the model compared to SGWR. In addition, the SGWR-GD stably determined the global optimal solution for each parameter. Simultaneously, the distribution of local residuals was also more stable.

与地理加权回归（GWR）不同，相似度和地理加权回归（SGWR）利用属性和地理相似度计算权重，从而有效地提高了模型的准确性。但是，SGWR不设置属性相似带宽。这导致其无法测量特征空间中空间过程的变化尺度。此外，由于采用的求解方法，SGWR可能陷入局部最优。为了解决这些问题，本研究提出了一种改进的相似度和地理加权回归模型（SGWR-GD），该模型在属性相似度核函数中增加了带宽。该参数使SGWR-GD能够在属性维度上度量空间过程的变化尺度，从而增强建模的灵活性。在求解模型时，SGWR-GD首先计算模型的修正赤池信息准则（Modified Akaike Information Criterion, AICc）相对于两个带宽和冲击比的梯度。随后，基于带框约束的梯度下降算法，得到了模型的全局最优解。将SGWR- gd和SGWR应用于5个不同的数据集，并比较了它们的拟合结果的精度。与SGWR相比，SGWR- gd显著提高了模型的精度。此外，SGWR-GD稳定地确定了各参数的全局最优解。同时，局部残差的分布也更加稳定。

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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 : 2025-03-28 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

Fast computation of the statistical significance test for spatio-temporal receptive field estimates obtained using spike-triggered averaging of binary pseudo-random sequences 基于脉冲触发二值伪随机序列的时空感受野估计统计显著性检验的快速计算

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-03-27 DOI: 10.1016/j.spasta.2025.100899

Murat Okatan

Background

Spatio-temporal receptive fields (STRFs) of visual neurons are often estimated using spike-triggered averaging (STA) with binary pseudo-random stimulus sequences. An exact analytical test—called the STA-BPRS test—has been developed to determine the statistical significance of each pixel in the STRF estimate. However, computing this test can take minutes to days, or even longer, for certain neurons.

New method

Here, the STA-BPRS test is accelerated by approximating the null distribution of STRF pixel estimates with a Normal distribution. This methodological refinement significantly reduces computation time, making large-scale data analysis feasible.

Results

The approximate test is systematically validated on real mouse retinal ganglion cell data and synthetic spike train data, demonstrating that it yields identical significance thresholds to the exact test. For neurons where, exact computation would be prohibitively long (e.g., hundreds of years), the approximate test completes in seconds or minutes.

Comparison with existing methods

Few approaches address pixel-by-pixel significance in STA-based STRF estimates. While subspace methods like spike-triggered covariance exist for STRF estimation, they typically do not provide direct voxel-wise or pixel-wise p-values. The proposed method specifically accelerates an exact distribution-based test.

Conclusions and impact

The proposed Normal approximation drastically reduces computation time, enabling high-throughput analysis of STRF mapping from spike data. This advancement may foster broader adoption of precise statistical tests of STRFs in large-scale, high-density electrophysiological recordings. Moreover, fast detection of significant STRF features could facilitate closed-loop experiments where stimuli dynamically adapt to changing STRF structures.

背景：视觉神经元的时空感受野（strf）通常是用二值伪随机刺激序列的spike-triggered averaging （STA）来估计的。已经开发了一种精确的分析测试，称为STA-BPRS测试，以确定STRF估计中每个像素的统计显著性。然而，对于某些神经元来说，计算这个测试可能需要几分钟到几天，甚至更长时间。本文通过用正态分布近似STRF像素估计的零分布来加速STA-BPRS检验。这种方法的改进大大减少了计算时间，使大规模数据分析成为可能。结果在真实小鼠视网膜神经节细胞数据和合成脉冲序列数据上系统地验证了近似测试，表明它与精确测试产生相同的显著性阈值。对于神经元，精确的计算将会非常长（例如，数百年），近似的测试在几秒钟或几分钟内完成。与现有方法的比较很少有方法可以解决基于sta的STRF估计中逐像素的显著性问题。虽然存在像尖峰触发协方差这样的子空间方法用于STRF估计，但它们通常不能提供直接的体素或像素p值。该方法特别加速了基于精确分布的测试。结论和影响所提出的正态近似大大减少了计算时间，使高通量分析STRF映射从峰值数据。这一进展可能促进在大规模高密度电生理记录中更广泛地采用精确的strf统计测试。此外，快速检测重要的STRF特征可以促进闭环实验，其中刺激动态适应变化的STRF结构。

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引用次数: 0

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 : 2025-03-26 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 : 2025-03-13 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

Bayesian adaptive Lasso estimation for partially linear hierarchical spatial autoregressive model 部分线性层次空间自回归模型的贝叶斯自适应Lasso估计

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-03-12 DOI: 10.1016/j.spasta.2025.100892

Miao Long, Zhimeng Sun

This paper presents a Bayesian adaptive Lasso estimation approach for partially linear hierarchical spatial autoregressive models. Despite advancements in spatial modeling, two key gaps remain: the lack of non-linear components in hierarchical spatial autoregressive models to capture complex spatial relationships, and the insufficient application of dimensionality reduction techniques to address high-dimensionality and overfitting. This paper addresses these issues by combining partially linear models with spatial autoregressive structures and incorporating dimensionality reduction techniques to enhance model efficiency and mitigate overfitting. The hierarchical structure facilitates multi-level modeling, accommodating complex data relationships. The Bayesian adaptive Lasso technique ensures effective variable selection and regularization, improving model interpretability and performance. Simulations and real data applications demonstrate the proposed method’s excellent performance. This work offers valuable insights for researchers and practitioners in dealing with spatially correlated data in various fields.

针对部分线性层次空间自回归模型，提出了一种贝叶斯自适应Lasso估计方法。尽管在空间建模方面取得了进步，但仍然存在两个关键差距：层次空间自回归模型中缺乏非线性成分来捕捉复杂的空间关系，以及降维技术在解决高维和过拟合问题上的应用不足。本文通过将部分线性模型与空间自回归结构相结合，并结合降维技术来提高模型效率和减轻过拟合，从而解决了这些问题。层次结构有助于多级建模，适应复杂的数据关系。贝叶斯自适应Lasso技术确保了有效的变量选择和正则化，提高了模型的可解释性和性能。仿真和实际数据应用证明了该方法的优良性能。这项工作为研究人员和实践者在处理各个领域的空间相关数据提供了有价值的见解。

引用次数: 0

Bayesian analysis and variable selection for spatial count data with an application to Rio de Janeiro gun violence 空间计数数据的贝叶斯分析与变量选择——以里约热内卢枪支暴力为例

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-02-27 DOI: 10.1016/j.spasta.2025.100890

Guilherme Ludwig , Yuan Wang , Tingjin Chu , Haonan Wang , Jun Zhu

Statistical analysis has been successfully applied to crime data for identification of crime hot spots and prediction of future crimes. In this paper, our main objective is to identify key factors for gun violence in Rio de Janeiro and study the relationship between these key factors and the number of reported events. We use a Bayesian hierarchical stochastic Poisson regression model for spatial counts, which enables us to address the over-dispersed count data and to handle the spatial correlation. Moreover, we propose a variable selection method for key factor identification based on the spike-and-slab prior distribution for the regression coefficients. A new Gibbs sampler is developed for sampling from the posterior distributions with the help of augmentation of Pólya-Gamma auxiliary variables. Simulation studies are used to demonstrate the performance of our proposed approach. Our analysis of the gun violence data in Rio de Janeiro reveals the relationship between violence events and socio-demographic covariates as well as an interpretable spatial random effect that accounts for unmeasured covariate information.

统计分析已成功地应用于犯罪数据中，用于识别犯罪热点和预测未来犯罪。在本文中，我们的主要目标是确定巴西里约热内卢枪支暴力的关键因素，并研究这些关键因素与报告事件数量之间的关系。我们使用贝叶斯分层随机泊松回归模型进行空间计数，这使我们能够解决过度分散的计数数据并处理空间相关性。此外，我们还提出了一种基于回归系数的穗板先验分布的变量选择方法来识别关键因素。利用Pólya-Gamma辅助变量的增广，开发了一种新的Gibbs采样器，用于对后验分布进行采样。仿真研究证明了我们提出的方法的性能。我们对巴西里约热内卢枪支暴力数据的分析揭示了暴力事件与社会人口协变量之间的关系，以及一种可解释的空间随机效应，该效应解释了不可测量的协变量信息。

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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 : 2025-02-24 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

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 : 2025-02-22 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

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