Pub Date : 2024-10-31DOI: 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。
{"title":"Uncovering hidden alignments in two-dimensional point fields","authors":"Eulogio Pardo-Igúzquiza , Peter A. Dowd","doi":"10.1016/j.spasta.2024.100868","DOIUrl":"10.1016/j.spasta.2024.100868","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-30DOI: 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.
{"title":"Spatio-temporal data fusion for the analysis of in situ and remote sensing data using the INLA-SPDE approach","authors":"Shiyu He, Samuel W.K. Wong","doi":"10.1016/j.spasta.2024.100863","DOIUrl":"10.1016/j.spasta.2024.100863","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-24DOI: 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.
{"title":"Exploiting nearest-neighbour maps for estimating the variance of sample mean in equal-probability systematic sampling of spatial populations","authors":"Sara Franceschi , Lorenzo Fattorini , Timothy G Gregoire","doi":"10.1016/j.spasta.2024.100865","DOIUrl":"10.1016/j.spasta.2024.100865","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-16DOI: 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.
{"title":"Variable selection of nonparametric spatial autoregressive models via deep learning","authors":"Xiaodi Zhang, Yunquan Song","doi":"10.1016/j.spasta.2024.100862","DOIUrl":"10.1016/j.spasta.2024.100862","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-02DOI: 10.1016/j.spasta.2024.100861
Zhi Zhang , Ruochen Mei , Changlin Mei
Geographically and temporally weighted regression (GTWR) models have been an effective tool for exploring spatiotemporal heterogeneity of regression relationships. However, they cannot effectively model such response variables that follows discrete distributions. In this study, we first extend the distributions of response variables to one-parameter exponential family of distributions and formulate generalized geographically and temporally weighted regression (GGTWR) models with their unilaterally temporally weighted maximum likelihood estimation method. Furthermore, we propose so-called multi-effect GGTWR (MEGGTWR) models in which spatiotemporally varying, constant, temporally varying, and spatially varying coefficients may simultaneously be included to reflect different effects of explanatory variables. A coefficient-average-based estimation method is suggested to calibrate MEGGTWR models and a generalized likelihood ratio statistic based test is formulated to identify the types of coefficients. Simulation studies are then conducted to assess the performance of the proposed estimation and inference methods with the impact of multicollinearity among explanatory variables also examined. The results show that the estimation method for MEGGTWR models can accurately estimate various types of coefficients and the test method is of valid type error and satisfactory power. Finally, the relationship between childhood hand, foot, and mouth disease cases and climate factors is analyzed by the proposed models with their estimation and inference methods and some interesting spatiotemporal patterns are uncovered.
地理和时间加权回归（GTWR）模型一直是探索回归关系时空异质性的有效工具。然而，它们不能有效地模拟这类遵循离散分布的响应变量。在本研究中，我们首先将响应变量的分布扩展到单参数指数分布族，并利用其单边时间加权最大似然估计方法建立广义地理和时间加权回归（GGTWR）模型。此外，我们还提出了所谓的多效应 GGTWR（MEGGTWR）模型，其中可同时包含时空变化系数、常数系数、时间变化系数和空间变化系数，以反映解释变量的不同效应。建议采用基于系数平均值的估计方法来校准 MEGGTWR 模型，并制定了基于广义似然比统计量的检验方法来识别系数类型。然后进行了模拟研究，以评估所提出的估计和推理方法的性能，并考察了解释变量之间多重共线性的影响。结果表明，MEGGTWR 模型的估计方法能准确估计各类系数，检验方法的 I 型误差有效，功率令人满意。最后，利用提出的模型及其估计和推理方法分析了儿童手足口病病例与气候因素之间的关系，发现了一些有趣的时空规律。
{"title":"Estimation and inference of multi-effect generalized geographically and temporally weighted regression models","authors":"Zhi Zhang , Ruochen Mei , Changlin Mei","doi":"10.1016/j.spasta.2024.100861","DOIUrl":"10.1016/j.spasta.2024.100861","url":null,"abstract":"<div><div>Geographically and temporally weighted regression (GTWR) models have been an effective tool for exploring spatiotemporal heterogeneity of regression relationships. However, they cannot effectively model such response variables that follows discrete distributions. In this study, we first extend the distributions of response variables to one-parameter exponential family of distributions and formulate generalized geographically and temporally weighted regression (GGTWR) models with their unilaterally temporally weighted maximum likelihood estimation method. Furthermore, we propose so-called multi-effect GGTWR (MEGGTWR) models in which spatiotemporally varying, constant, temporally varying, and spatially varying coefficients may simultaneously be included to reflect different effects of explanatory variables. A coefficient-average-based estimation method is suggested to calibrate MEGGTWR models and a generalized likelihood ratio statistic based test is formulated to identify the types of coefficients. Simulation studies are then conducted to assess the performance of the proposed estimation and inference methods with the impact of multicollinearity among explanatory variables also examined. The results show that the estimation method for MEGGTWR models can accurately estimate various types of coefficients and the test method is of valid type <span><math><mi>I</mi></math></span> error and satisfactory power. Finally, the relationship between childhood hand, foot, and mouth disease cases and climate factors is analyzed by the proposed models with their estimation and inference methods and some interesting spatiotemporal patterns are uncovered.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-30DOI: 10.1016/j.spasta.2024.100860
Véronique Maume-Deschamps , Pierre Ribereau , Manal Zeidan
Few spatio-temporal models allow temporal non-stationarity. When modeling environmental data recorded over the last decades of the 20th century until now, it seems not reasonable to assume temporal stationarity, since it would not capture climate change effects. In this paper, we propose a space–time max-stable model for modeling some temporal non-stationarity of the spatial extremal dependence. Our model consists of a mixture of max-stable spatial processes, with a rate of mixing depending on time. We use maximum composite likelihood for estimation, model selection, and a non-stationarity test. The assessment of its performance is done through wide simulation experiments. The proposed model is used to investigate how the rainfall in the south of France evolves with time. The results demonstrate that the spatial extremal dependence is significantly non-stationary over time, with a decrease in the strength of dependence.
{"title":"A spatio-temporal model for temporal evolution of spatial extremal dependence","authors":"Véronique Maume-Deschamps , Pierre Ribereau , Manal Zeidan","doi":"10.1016/j.spasta.2024.100860","DOIUrl":"10.1016/j.spasta.2024.100860","url":null,"abstract":"<div><div>Few spatio-temporal models allow temporal non-stationarity. When modeling environmental data recorded over the last decades of the 20th century until now, it seems not reasonable to assume temporal stationarity, since it would not capture climate change effects. In this paper, we propose a space–time max-stable model for modeling some temporal non-stationarity of the spatial extremal dependence. Our model consists of a mixture of max-stable spatial processes, with a rate of mixing depending on time. We use maximum composite likelihood for estimation, model selection, and a non-stationarity test. The assessment of its performance is done through wide simulation experiments. The proposed model is used to investigate how the rainfall in the south of France evolves with time. The results demonstrate that the spatial extremal dependence is significantly non-stationary over time, with a decrease in the strength of dependence.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1016/j.spasta.2024.100858
Chiara Fend, Claudia Redenbach
In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on asymptotics or on Monte Carlo simulation of a parametric null model. Here, we present a nonparametric test based on resampling the Fry points of the observed point pattern. Empirical levels and powers of the test are investigated in a simulation study for four point process models with anisotropy induced by different mechanisms. Finally, a real data set is tested for isotropy.
{"title":"Nonparametric isotropy test for spatial point processes using random rotations","authors":"Chiara Fend, Claudia Redenbach","doi":"10.1016/j.spasta.2024.100858","DOIUrl":"10.1016/j.spasta.2024.100858","url":null,"abstract":"<div><p>In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on asymptotics or on Monte Carlo simulation of a parametric null model. Here, we present a nonparametric test based on resampling the Fry points of the observed point pattern. Empirical levels and powers of the test are investigated in a simulation study for four point process models with anisotropy induced by different mechanisms. Finally, a real data set is tested for isotropy.</p></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2211675324000496/pdfft?md5=ecd689cca4efc52769fb4d5c74c41dab&pid=1-s2.0-S2211675324000496-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142271892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-04DOI: 10.1016/j.spasta.2024.100857
Septian Rahardiantoro, Sachnaz Desta Oktarina, Anang Kurnia, Nickyta Shavira Maharani, Alfidhia Rahman Nasa Juhanda
Indonesia is a country that has been greatly affected by the Covid-19 pandemic. In the almost three years that the pandemic has been going on, the spread of Covid-19 has penetrated almost all regions of Indonesia. One of the causes of the rapid spread of Covid-19 confirmed cases in Indonesia is the existence of domestic flights between regions within the archipelago. This research is aimed to identify patterns of Covid-19 transmission cases between provinces in Indonesia using spatio-temporal clustering. The method used a generalized lasso approach based on flight connections and proximity between provinces. The results suggested that clustering based on flight connections between provinces obtained more reasonable results, namely that there were three clusters of provinces formed with different patterns of spread of Covid-19 cases over time.
{"title":"Spatio-temporal clustering using generalized lasso to identify the spread of Covid-19 in Indonesia according to provincial flight route-based connections","authors":"Septian Rahardiantoro, Sachnaz Desta Oktarina, Anang Kurnia, Nickyta Shavira Maharani, Alfidhia Rahman Nasa Juhanda","doi":"10.1016/j.spasta.2024.100857","DOIUrl":"10.1016/j.spasta.2024.100857","url":null,"abstract":"<div><p>Indonesia is a country that has been greatly affected by the Covid-19 pandemic. In the almost three years that the pandemic has been going on, the spread of Covid-19 has penetrated almost all regions of Indonesia. One of the causes of the rapid spread of Covid-19 confirmed cases in Indonesia is the existence of domestic flights between regions within the archipelago. This research is aimed to identify patterns of Covid-19 transmission cases between provinces in Indonesia using spatio-temporal clustering. The method used a generalized lasso approach based on flight connections and proximity between provinces. The results suggested that clustering based on flight connections between provinces obtained more reasonable results, namely that there were three clusters of provinces formed with different patterns of spread of Covid-19 cases over time.</p></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142230126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-17DOI: 10.1016/j.spasta.2024.100856
Christopher K. Wikle , Mevin B. Hooten , William Kleiber , Douglas W. Nychka
{"title":"Spatial statistics: Climate and the environment","authors":"Christopher K. Wikle , Mevin B. Hooten , William Kleiber , Douglas W. Nychka","doi":"10.1016/j.spasta.2024.100856","DOIUrl":"10.1016/j.spasta.2024.100856","url":null,"abstract":"","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-14DOI: 10.1016/j.spasta.2024.100855
Daniel A. Griffith
This paper marks the 50-year publication anniversary of Besag's seminal spatial auto- models paper. His classic article synthesizes generic autoregressive specifications (i.e., a response variable appears on both sides of a regression equation and/or probability function equal sign) for the following six popular random variables: normal, logistic (i.e., Bernoulli), binomial, Poisson, exponential, and gamma. Besag dismisses these last two while recognizing failures of both as well as the more scientifically critical counts-oriented auto-Poisson. His initially unsuccessful subsequent work first attempted to repair them (e.g., pseudo-likelihood estimation), and then successfully revise them within the context of mixed models, formulating a spatially structured random effects term that effectively and efficiently absorbs and accounts for spatial autocorrelation in geospatial data. One remaining weakness of all but the auto-normal is a need to resort to Markov chain Monte Carlo (MCMC) techniques for legitimate estimation purposes. Recently, Griffith succeeded in devising an innovative uniform distribution genre—sui-uniform random variables—that accommodates spatial autocorrelation, too. Its most appealing feature is that, by applying two powerful mathematical statistical theorems (i.e., the probability integral transform, and the quantile function), it redeems Besag's auto- model failures. This paper details conversion of Besag's initial six modified variates, exemplifying them with both simulation experiments and publicly accessible real-world georeferenced data. The principal outcome is valuable spatial statistical advancements, with special reference to Moran eigenvector spatial filtering.
{"title":"Self-correlated spatial random variables: From an auto- to a sui- model respecification","authors":"Daniel A. Griffith","doi":"10.1016/j.spasta.2024.100855","DOIUrl":"10.1016/j.spasta.2024.100855","url":null,"abstract":"<div><p>This paper marks the 50-year publication anniversary of Besag's seminal spatial auto- models paper. His classic article synthesizes generic autoregressive specifications (i.e., a response variable appears on both sides of a regression equation and/or probability function equal sign) for the following six popular random variables: normal, logistic (i.e., Bernoulli), binomial, Poisson, exponential, and gamma. Besag dismisses these last two while recognizing failures of both as well as the more scientifically critical counts-oriented auto-Poisson. His initially unsuccessful subsequent work first attempted to repair them (e.g., pseudo-likelihood estimation), and then successfully revise them within the context of mixed models, formulating a spatially structured random effects term that effectively and efficiently absorbs and accounts for spatial autocorrelation in geospatial data. One remaining weakness of all but the auto-normal is a need to resort to Markov chain Monte Carlo (MCMC) techniques for legitimate estimation purposes. Recently, Griffith succeeded in devising an innovative uniform distribution genre—sui-uniform random variables—that accommodates spatial autocorrelation, too. Its most appealing feature is that, by applying two powerful mathematical statistical theorems (i.e., the probability integral transform, and the quantile function), it redeems Besag's auto- model failures. This paper details conversion of Besag's initial six modified variates, exemplifying them with both simulation experiments and publicly accessible real-world georeferenced data. The principal outcome is valuable spatial statistical advancements, with special reference to Moran eigenvector spatial filtering.</p></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142083754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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