Spatial Statistics最新文献

英文中文

Simulation of conditional non-Gaussian random fields with directional asymmetry 模拟具有方向不对称性的条件非高斯随机场

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-11-17 DOI: 10.1016/j.spasta.2024.100872

Sebastian Hörning , András Bárdossy

Observed environmental are usually the results of physical, chemical, or biological processes. These processes often introduce asymmetries which should be considered when analysing and modelling the observed variables. In a geostatistical context, there are two main types of asymmetry. The first is rank-asymmetry, i.e., low and high values exhibit different spatial dependence structures. The second is order-asymmetry, i.e., the spatial dependence structure is distinguishable in different directions. Both asymmetries, if significant, indicate that the corresponding random field has a non-Gaussian dependence structure. These asymmetries are not part of the classical geostatistical workflow. Taking asymmetry into account however is likely to improve the estimation and the uncertainty assessment at unobserved locations. In this contribution a stochastic model which can be used to simulate asymmetrical random fields with any of the asymmetries or with their combination is presented. Synthetically simulated flow fields and the well known Walker lake dataset are used to demonstrate the methodology.

观测到的环境通常是物理、化学或生物过程的结果。这些过程通常会带来不对称现象，在分析和模拟观测变量时应加以考虑。在地统计学中，不对称主要有两种类型。第一种是等级不对称，即低值和高值表现出不同的空间依赖结构。第二种是阶次不对称，即空间依赖结构在不同方向上有区别。如果这两种不对称现象显著，则表明相应的随机场具有非高斯依赖结构。这些非对称性不属于经典的地质统计工作流程。然而，将非对称性考虑在内很可能会改进未观测地点的估算和不确定性评估。本文介绍了一个随机模型，该模型可用于模拟任何一种不对称或其组合的不对称随机场。合成模拟的流场和众所周知的沃克湖数据集用于演示该方法。

引用次数: 0

Joint spatial modeling of mean and non-homogeneous variance combining semiparametric SAR and GAMLSS models for hedonic prices 结合半参数 SAR 模型和 GAMLSS 模型为对冲价格建立均值和非均质方差的联合空间模型

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-11-16 DOI: 10.1016/j.spasta.2024.100864

J.D. Toloza-Delgado , O.O. Melo , N.A. Cruz

In the context of spatial econometrics, it is very useful to have methodologies that allow modeling the spatial dependence of the observed variables and obtaining more precise predictions of both the mean and the variability of the response variable, something very useful in territorial planning and public policies. This paper proposes a new methodology that jointly models the mean and the variance. Also, it allows to model the spatial dependence of the dependent variable as a function of covariates and to model the semiparametric effects in both models. The algorithms developed are based on generalized additive models that allow the inclusion of non-parametric terms in both the mean and the variance, maintaining the traditional theoretical framework of spatial regression. The theoretical developments of the estimation of this model are carried out, obtaining desirable statistical properties in the estimators. A simulation study is developed to verify that the proposed method has a remarkable predictive capacity in terms of the mean square error and shows a notable improvement in the estimation of the spatial autoregressive parameter, compared to other traditional methods and some recent developments. The model is also tested on data from the construction of a hedonic price model for the city of Bogotá, highlighting as the main result the ability to model the variability of housing prices, and the wealth in the analysis obtained.

在空间计量经济学中，有一种方法可以对观测变量的空间依赖性进行建模，并对响应变量的均值和变异性进行更精确的预测，这对领土规划和公共政策非常有用。本文提出了一种联合模拟均值和方差的新方法。此外，它还可以将因变量的空间依赖性作为协变量的函数进行建模，并在两个模型中对半参数效应进行建模。所开发的算法基于广义加法模型，允许在均值和方差中包含非参数项，保持了空间回归的传统理论框架。对该模型的估计进行了理论开发，在估计器中获得了理想的统计特性。通过模拟研究，验证了所提出的方法在均方误差方面具有显著的预测能力，与其他传统方法和一些最新方法相比，在空间自回归参数估计方面有明显改善。该模型还对波哥大市构建保值价格模型的数据进行了测试，其主要结果是突出了对住房价格变化的建模能力，以及所获分析的丰富性。

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引用次数: 0

Epidemiological insights and geographic clusters for COVID-19 in Taiwan using a mixture scan statistic 利用混合扫描统计法洞察台湾 COVID-19 的流行病学和地理集群

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-11-13 DOI: 10.1016/j.spasta.2024.100871

Yi-Hung Kung

The COVID-19 pandemic has posed unprecedented public health challenges worldwide, necessitating a comprehensive understanding of its transmission dynamics. This study examines the correlation between COVID-19 transmission and various risk factors, focusing on the impact of population structure and socio-economic conditions in Taiwan. By analyzing official government databases, we explore how factors such as population density, dependency ratios, and socio-economic environment influence the spread of COVID-19. Our findings highlight that densely populated areas, along with regions characterized by higher child dependency ratios and a significant number of low- and middle-income households, exhibit higher transmission rates. This research underscores the importance of considering socio-economic disparities and healthcare access in developing effective public health strategies. Furthermore, we utilize a mixture scan statistic to identify disease hotspots, taking into account spatial correlation and covariate effects. This approach can detect clusters based on known risk factors and help to assess possible unknown geographic risks, facilitating targeted interventions and resource allocation. Our study contributes to the broader understanding of COVID-19 transmission dynamics, offering insights into the importance of integrating socio-economic factors and spatial analysis in pandemic response efforts.

COVID-19 大流行给全球公共卫生带来了前所未有的挑战，因此有必要全面了解其传播动态。本研究探讨了 COVID-19 传播与各种风险因素之间的相关性，重点关注台湾人口结构和社会经济条件的影响。通过分析政府官方数据库，我们探讨了人口密度、抚养比和社会经济环境等因素如何影响 COVID-19 的传播。我们的研究结果表明，人口稠密地区、儿童抚养比高的地区以及中低收入家庭较多的地区的传播率较高。这项研究强调了在制定有效的公共卫生策略时考虑社会经济差异和医疗保健服务的重要性。此外，考虑到空间相关性和协变量效应，我们利用混合扫描统计来识别疾病热点。这种方法可以根据已知的风险因素发现疾病集群，并有助于评估可能存在的未知地理风险，从而促进有针对性的干预措施和资源分配。我们的研究有助于人们更广泛地了解 COVID-19 的传播动态，为在大流行病应对工作中整合社会经济因素和空间分析的重要性提供了启示。

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引用次数: 0

A flexible class of priors for orthonormal matrices with basis function-specific structure 一类灵活的正交矩阵先验，具有基函数特定结构

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-11-12 DOI: 10.1016/j.spasta.2024.100866

Joshua S. North , Mark D. Risser , F. Jay Breidt

Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly factor the original data into the product of orthonormal basis functions and weights, where each basis function represents an independent feature of the data. However, the basis functions in these factorizations are typically computed using algorithmic methods that cannot quantify uncertainty or account for basis function correlation structure a priori. While there exist Bayesian methods that allow for a common correlation structure across basis functions, empirical examples motivate the need for basis function-specific dependence structure. We propose a prior distribution for orthonormal matrices that can explicitly model basis function-specific structure. The prior is used within a general probabilistic model for singular value decomposition to conduct posterior inference on the basis functions while accounting for measurement error and fixed effects. We discuss how the prior specification can be used for various scenarios and demonstrate favorable model properties through synthetic data examples. Finally, we apply our method to two-meter air temperature data from the Pacific Northwest, enhancing our understanding of the Earth system’s internal variability.

高维矩阵值数据的统计建模需要使用低秩表示法，这种表示法既能概括数据的关键特征，又能降低维数。低秩表示通常将原始数据分解为正交基函数和权重的乘积，其中每个基函数代表数据的一个独立特征。然而，这些因式分解中的基函数通常使用算法方法计算，无法量化不确定性，也无法预先考虑基函数的相关结构。虽然有贝叶斯方法允许基函数之间存在共同的相关结构，但经验实例表明需要特定于基函数的依赖结构。我们提出了一种正交矩阵的先验分布，可以明确地模拟特定于基函数的结构。该先验分布可用于奇异值分解的一般概率模型，在考虑测量误差和固定效应的同时，对基函数进行后验推断。我们讨论了如何在各种情况下使用先验规范，并通过合成数据示例展示了有利的模型特性。最后，我们将我们的方法应用于西北太平洋地区的两米气温数据，从而加深我们对地球系统内部变异性的理解。

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引用次数: 0

Regularization of the Ensemble Kalman Filter using a non-parametric, non-stationary spatial model 利用非参数、非稳态空间模型对集合卡尔曼滤波器进行规范化处理

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-11-09 DOI: 10.1016/j.spasta.2024.100870

Michael Tsyrulnikov , Arseniy Sotskiy

The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in high dimensions the Ensemble Kalman Filter’s (EnKF) ensemble does not contain enough information to specify the prior covariance matrix accurately. This necessitates the need for regularization of the analysis (observation update) problem. We propose a regularization technique based on a new spatial model. The model is a constrained version of the general Gaussian process convolution model. The constraints include local stationarity and smoothness of local spectra. We regularize EnKF by postulating that its prior covariances obey the spatial model. Placing a hyperprior distribution on the model parameters and using the likelihood of the prior ensemble data allows for an optimized use of both the ensemble and the hyperprior. A linear version of the respective estimator is shown to be consistent. A more accurate nonlinear neural-Bayes implementation of the estimator is developed. In simulation experiments, the new technique led to substantially better EnKF performance than several existing techniques.

如果样本量远大于向量的长度，那么随机向量的样本协方差矩阵就是真实协方差矩阵的良好估计值。在高维问题中，这一条件永远无法满足。因此，在高维情况下，卡尔曼滤波器（EnKF）的集合不包含足够的信息来准确指定先验协方差矩阵。这就需要对分析（观测更新）问题进行正则化。我们提出了一种基于新空间模型的正则化技术。该模型是一般高斯过程卷积模型的约束版本。约束条件包括局部静止性和局部频谱的平滑性。我们假设 EnKF 的先验协方差服从空间模型，从而对 EnKF 进行正则化。在模型参数上放置超先验分布，并使用先验集合数据的似然性，可以优化集合和超先验的使用。研究表明，各自估计器的线性版本是一致的。我们还开发了一种更精确的非线性神经贝叶斯估计器。在模拟实验中，新技术的 EnKF 性能大大优于现有的几种技术。

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引用次数: 0

Non-stationary spatio-temporal modeling using the stochastic advection–diffusion equation 利用随机平流扩散方程进行非稳态时空建模

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-11-06 DOI: 10.1016/j.spasta.2024.100867

Martin Outzen Berild, Geir-Arne Fuglstad

We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation of the solution of the SPDE, which is constructed through a finite volume method. The new flexible non-separable model is compared to a flexible separable model both for reconstruction and forecasting, and evaluated in terms of root mean square errors and continuous rank probability scores. A simulation study demonstrates that the non-separable model performs better when the data is simulated from a non-separable model with diffusion and advection. Further, we estimate surrogate models for emulating the output of a ocean model in Trondheimsfjorden, Norway, and simulate observations of autonomous underwater vehicles. The results show that the flexible non-separable model outperforms the flexible separable model for real-time prediction of unobserved locations.

我们通过随机偏微分方程（SPDE）构建了灵活的时空模型，其中扩散和平流都可以在空间上变化。计算是通过有限体积法构建的 SPDE 解的高斯马尔可夫随机场近似来完成的。在重建和预测方面，新的灵活的不可分离模型与灵活的可分离模型进行了比较，并以均方根误差和连续等级概率分数进行了评估。模拟研究表明，当数据从一个具有扩散和平流的不可分离模型模拟时，不可分离模型的性能更好。此外，我们还估算了用于模拟挪威特隆赫姆斯峡湾海洋模型输出的代用模型，并模拟了自主水下航行器的观测结果。结果表明，在对未观测地点进行实时预测方面，灵活的不可分割模型优于灵活的可分离模型。

引用次数: 0

Uncovering hidden alignments in two-dimensional point fields 揭示二维点域中的隐藏排列

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-10-31 DOI: 10.1016/j.spasta.2024.100868

Eulogio Pardo-Igúzquiza , Peter A. Dowd

The problem of mapping hidden alignments of points in data sets of two-dimensional points is of significant interest in many geoscience disciplines. In this paper, we revisit this issue and provide a new algorithm, insights, and results. The statistical significance of alignments is assessed by using percentile confidence intervals estimated by a Monte Carlo procedure in which important issues, such as the shape of the geometric support and the possible non-homogeneity of the point density (i.e., clustering effects), have been considered. The procedure is not limited to the simplest case of occurrence and the chance of triads (alignments of three points in a plane) but has been extended to k-ads with k arbitrarily large. The important issue of scale, when searching for point alignments, has also been taken into account. Case studies using synthetic and real data sets are provided to illustrate the methodology and the claims.

绘制二维点数据集中点的隐藏排列图是许多地球科学学科非常感兴趣的问题。在本文中，我们重新审视了这一问题，并提供了一种新的算法、见解和结果。通过使用蒙特卡罗程序估算的百分位数置信区间来评估排列的统计意义，其中考虑了一些重要问题，如几何支撑的形状和点密度可能存在的非均质性（即聚类效应）。该程序并不局限于最简单的三元组（平面上三个点的排列）出现和出现的几率，而是扩展到了 k 值任意大的 k 元组。在搜索点排列时，还考虑到了重要的规模问题。我们提供了使用合成数据集和真实数据集的案例研究，以说明我们的方法和主张。

引用次数: 0

Spatio-temporal data fusion for the analysis of in situ and remote sensing data using the INLA-SPDE approach 利用 INLA-SPDE 方法进行时空数据融合，以分析原地数据和遥感数据

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-10-30 DOI: 10.1016/j.spasta.2024.100863

Shiyu He, Samuel W.K. Wong

We propose a Bayesian hierarchical model to address the challenge of spatial misalignment in spatio-temporal data obtained from in situ and satellite sources. The model is fit using the INLA-SPDE approach, which provides efficient computation. Our methodology combines the different data sources in a “fusion” model via the construction of projection matrices in both spatial and temporal domains. Through simulation studies, we demonstrate that the fusion model has superior performance in prediction accuracy across space and time compared to standalone “in situ” and “satellite” models based on only in situ or satellite data, respectively. The fusion model also generally outperforms the standalone models in terms of parameter inference. Such a modeling approach is motivated by environmental problems, and our specific focus is on the analysis and prediction of harmful algae bloom (HAB) events, where the convention is to conduct separate analyses based on either in situ samples or satellite images. A real data analysis shows that the proposed model is a necessary step towards a unified characterization of bloom dynamics and identifying the key drivers of HAB events.

我们提出了一个贝叶斯分层模型，以解决从原地和卫星来源获得的时空数据中存在的空间错位问题。该模型采用 INLA-SPDE 方法拟合，计算效率高。我们的方法通过构建空间和时间域的投影矩阵，将不同的数据源结合到一个 "融合 "模型中。通过模拟研究，我们证明，与仅基于原地数据或卫星数据的独立 "原地 "模型和 "卫星 "模型相比，融合模型在跨时空预测精度方面具有更优越的性能。在参数推断方面，融合模型也普遍优于独立模型。这种建模方法源于环境问题，我们的具体重点是有害藻华（HAB）事件的分析和预测，在这种情况下，传统的做法是根据原地样本或卫星图像分别进行分析。实际数据分析表明，所提出的模型是统一描述藻华动态和确定 HAB 事件关键驱动因素的必要步骤。

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引用次数: 0

Exploiting nearest-neighbour maps for estimating the variance of sample mean in equal-probability systematic sampling of spatial populations 利用近邻图估计空间种群等概率系统抽样中样本平均值的方差

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-10-24 DOI: 10.1016/j.spasta.2024.100865

Sara Franceschi , Lorenzo Fattorini , Timothy G Gregoire

Because of its ease of implementation, equal probability systematic sampling is of wide use in spatial surveys with sample mean that constitutes an unbiased estimator of population mean. A serious drawback, however, is that no unbiased estimator of the variance of the sample mean is available. As the search for an omnibus variance estimator able to provide reliable results under any spatial population has been lacking, we propose a design-consistent estimator that invariably converges to the true variance as the population and sample size increase. The proposal is based on the nearest-neighbour maps that are taken as pseudo-populations from which all the possible systematic samples can be enumerated. As nearest-neighbour maps are design-consistent under equal-probability systematic sampling and mild conditions, the variance of the sample mean achieved from all the possible systematic samples selected from the map is also a consistent estimator of the true variance. Through a simulation study based on artificial and real populations we show that our proposal generally outperforms the familiar estimators proposed in literature.

由于等概率系统抽样易于实施，因此在空间调查中得到广泛应用，其样本平均值是人口平均值的无偏估计值。然而，一个严重的缺点是，没有对样本平均数方差进行无偏估计的方法。我们一直在寻找一种能够在任何空间人口条件下提供可靠结果的综合方差估计器，因此我们提出了一种与设计一致的估计器，随着人口和样本量的增加，该估计器会不断趋近于真实方差。该建议以最近邻地图为基础，将其作为伪种群，从中列举出所有可能的系统样本。由于近邻地图在等概率系统抽样和温和条件下是设计一致的，因此从地图上选取的所有可能的系统抽样所得到的样本平均值的方差也是真实方差的一致估计值。通过基于人工和真实人群的模拟研究，我们表明我们的建议总体上优于文献中提出的熟悉估计器。

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引用次数: 0

Variable selection of nonparametric spatial autoregressive models via deep learning 通过深度学习选择非参数空间自回归模型的变量

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2024-10-16 DOI: 10.1016/j.spasta.2024.100862

Xiaodi Zhang, Yunquan Song

With the development of deep learning techniques, the application of neural networks to statistical inference has dramatically increased in popularity. In this paper, we extend the deep neural network-based variable selection method to nonparametric spatial autoregressive models. Our approach incorporates feature selection and parameter learning by introducing Lasso penalties in a residual network structure with spatial effects. We transform the problem into a constrained optimization task, where optimizing an objective function with constraints. Without specifying sparsity, we are also able to obtain a specific set of selected variables. The performance of the method with finite samples is demonstrated through an extensive Monte Carlo simulation study. Finally, we apply the method to California housing price data, further validating its superiority in terms of variable selection and predictive performance.

随着深度学习技术的发展，神经网络在统计推断中的应用急剧增加。在本文中，我们将基于深度神经网络的变量选择方法扩展到非参数空间自回归模型。我们的方法通过在具有空间效应的残差网络结构中引入 Lasso 惩罚，将特征选择和参数学习结合起来。我们将问题转化为约束优化任务，即优化具有约束条件的目标函数。在不指定稀疏性的情况下，我们也能获得一组特定的选定变量。通过广泛的蒙特卡罗模拟研究，我们证明了该方法在有限样本下的性能。最后，我们将该方法应用于加州住房价格数据，进一步验证了其在变量选择和预测性能方面的优越性。

引用次数: 0

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