Spatial Statistics最新文献

英文中文

Computationally efficient spatio-temporal disease mapping for big data 面向大数据的高效时空疾病制图

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-04-23 DOI: 10.1016/j.spasta.2025.100901

Duncan Lee

Disease mapping models estimate the spatio-temporal variation in population-level disease risks or rates across a set of

K

areal units for

N

time periods, aiming to identify temporal trends and spatial hotspots. Highly parameterised Bayesian hierarchical models with over

K N

random effects are commonly used to estimate this spatio-temporal variation, which are assigned autoregressive and conditional autoregressive prior distributions. These models work well when there are tens of thousands of data points, but are likely to be computationally burdensome when this rises to hundreds of thousands or above. This paper proposes a computationally efficient alternative, which can fit a range of spatio-temporal disease trends almost as well as existing highly parameterised models but only takes around 5% to 40% of the time to implement. It achieves this by modelling the average spatial and temporal trends in the data with autoregressive type random effects, which are augmented by an observation-driven process using functions of earlier data as additional covariates in the model. The efficacy of this methodology is tested by simulation, before being applied to the motivating study that estimates the spatio-temporal trends in asthma, cancer, coronary heart and chronic obstructive pulmonary disease prevalences for

K = 32, 751

small areas over

N = 13

years in England.

疾病制图模型估算了N个时间段内K个面积单位的人群水平疾病风险或发病率的时空变化，旨在确定时间趋势和空间热点。具有超过KN随机效应的高参数化贝叶斯层次模型通常用于估计这种时空变化，该模型被分配为自回归和条件自回归先验分布。当有数以万计的数据点时，这些模型工作得很好，但当数据点增加到数十万或更多时，计算负担可能会很重。本文提出了一种计算效率高的替代方案，它可以拟合一系列时空疾病趋势，几乎和现有的高度参数化模型一样，但只需要大约5%到40%的时间来实现。它通过用自回归型随机效应对数据中的平均空间和时间趋势进行建模来实现这一点，这些趋势通过使用早期数据的函数作为模型中的附加协变量的观测驱动过程来增强。该方法的有效性通过模拟测试，然后应用于一项激励研究，该研究估计了英国K=32,751个小地区在N=13年内哮喘、癌症、冠心病和慢性阻塞性肺病患病率的时空趋势。

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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 : 2025-04-15 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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引用次数: 0

Isotropy testing in spatial point patterns: nonparametric versus parametric replication under misspecification 空间点模式的各向同性测试：错误规范下的非参数与参数复制

IF 2.1 2区数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY

Spatial Statistics

Pub Date : 2025-04-05 DOI: 10.1016/j.spasta.2025.100898

Jakub J. Pypkowski, Adam M. Sykulski, James S. Martin

Several hypothesis testing methods have been proposed to validate the assumption of isotropy in spatial point patterns. A majority of these methods are characterised by an unknown distribution of the test statistic under the null hypothesis of isotropy. Parametric approaches to approximating the distribution involve simulation of patterns from a user-specified isotropic model. Alternatively, nonparametric replicates of the test statistic under isotropy can be used to waive the need for specifying a model. In this paper, we first present a general framework which allows for the integration of a selected nonparametric replication method into isotropy testing. We then conduct a large simulation study comprising application-like scenarios to assess the performance of tests with different parametric and nonparametric replication methods. In particular, we explore distortions in test size and power caused by model misspecification, and demonstrate the advantages of nonparametric replication in such scenarios.

为了验证空间点图的各向同性假设，提出了几种假设检验方法。大多数这些方法的特点是在各向同性的零假设下检验统计量的未知分布。逼近分布的参数化方法包括从用户指定的各向同性模型模拟模式。另外，可以使用各向同性下检验统计量的非参数重复来免除指定模型的需要。在本文中，我们首先提出了一个一般框架，该框架允许将选择的非参数复制方法集成到各向同性测试中。然后，我们进行了一个大型模拟研究，包括类似应用程序的场景，以评估不同参数和非参数复制方法的测试性能。特别地，我们探讨了由模型规格错误引起的测试尺寸和功率的扭曲，并展示了在这种情况下非参数复制的优势。

引用次数: 0

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

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