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This study compares the environmental sustainability of two cities in Saudi Arabia, Abha, and Bisha, through their green spaces, by analyzing green spaces in both cities. And the application of spatial statistics tools in the Arc Map program, to measure the spatial relationship between the green areas depending on the measurement of the location, shape, dimensions and areas, as this distribution is linked to statistical laws leading to the construction of a spatial model for the green areas in the two cities, and among these methods is the spatial average, The central phenomenon, the distribution trend, the standard circle, and finally the neighborhood analysis. The study seeks to recognize the parameters that contribute to environmental sustainability through green spaces. Understanding the effectiveness of green spaces in promoting environmental sustainability is crucial for policymakers to make informed decisions about urban planning and development. Sustainability in the environment is making responsible use of natural resources while also taking measures to safeguard the surrounding area to maintain high standards of environmental quality over the long term. The concept entails the preservation of equilibrium among economic, social, and environmental considerations to guarantee the satisfaction of current societal requirements while safeguarding the capacity of forthcoming generations to fulfill their own necessities. Environmental sustainability is crucial for the well-being of the planet and all living beings that inhabit it. Green spaces play a vital role in environmental sustainability. The provision of green spaces is associated with a multitude of advantages, including but not limited to the mitigation of air and noise pollution, temperature regulation, and enhancement of the overall visual appeal of urban areas. The study employed Geographic Information System (GIS) and spatial statistical analysis to investigate the spatial arrangement of environmental sustainability in the two urban areas. The study also relied on fieldwork, including a questionnaire, to gather data from the residents of the cities. The research study found that the standard distance measures the average distance between each green space and the mean center. In this case, the standard distance indicates how dispersed or clustered the green spaces are around the mean center. A smaller standard distance value suggests that the green spaces are more clustered around the mean center, while a larger value suggests a more dispersed distribution. [ABSTRACT FROM AUTHOR]

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Short wavelengths in the visible part of the electromagnetic spectrum ranging from (380-500) nm; which includes blue light, can trigger critical physiological responses including circadian rhythm synchronization and pupil constriction. Blue light cause damage to human eye, and the blue light hazard term has been coined to highlight this dangerous. The blue light can result in the demise of healthy tissue via apoptosis of photoreceptors and critical retinal pigment epithelial (RPE). This slow motion process during which damage accumulates over a lifetime has been embroiled in the different types of refractive errors i.e. (longsighted, shortsighted, and astigmatism) and pathogenesis of retinal degenerative diseases. In the present work, patients were chosen at random from different areas in Iraq and studied for the period from November 2016 to March 2017. The refractive errors of the eye were corrected using two different methods (traditional and blue light filter) spectacles. The blue-light filtering glasses were using for improving the vision of the patients and gave the best results for correction's compared with traditional glasses. This relationship was examined to investigate the potential correlation between the presence or absence of a blue filter on the refractive errors for the optics of the eye, and the inter-pupillary distance (IPD). Geo-spatial techniques were also utilized with the aid of Geographical Geographical Information System (GIS) software for analysis and interpretation of the acquired data over a wide range of Iraq. A new statistical model designed by us using Statistical Package for the Social Sciences (SPSS) to show if the results is significant or not significant. Results utilized with a statistically significant value less than 0.0001 for spherical-blue-filter, cylindrical-blue value, and axis-blue filter. [ABSTRACT FROM AUTHOR]

The definition of complexity through Statistical Complexity Measures (SCM) has recently seen major improvements. Mostly, the effort is concentrated in measures on time series. We propose a SCM definition for spatial dynamical systems. Our definition is in line with the trend to combine entropy with measures of structure (such as disequilibrium). We study the behaviour of our definition against the vectorial noise model of Collective Motion. From a global perspective, we show how our SCM is minimal at both the microscale and macroscale, while it reaches a maximum at the ranges that define the mesoscale in this model. From a local perspective, the SCM is minimum both in highly ordered and disordered areas, while it reaches a maximum at the edges between such areas. These characteristics suggest this is a good candidate for detecting the mesoscale of arbitrary dynamical systems as well as regions where the complexity is maximal in such systems. [ABSTRACT FROM AUTHOR]

Local spatial statistics measure and test for spatial association for a variable or variables of interest in a geographic neighborhood surrounding a predefined location. Most applications adopt a single scale of analysis but give little attention to the scale of the process generating the data. Alternatively, when the researcher is uncertain about the process scale, local statistics may examine a number of scales. In these cases, it is important to include a correction for multiple testing when evaluating the statistical significance of each local statistic, something that is rarely done. Consequently, local statistics are more likely to identify significant relationships, even when no meaningful spatial association exists. In this article, we develop a methodology for the local Moran statistic that provides both an empirical estimate of the spatial scale of association and an assessment of the significance of the statistic for that scale. The key idea is to test a number of possible choices for the statistic's weight matrix and then account for the multiple testing associated with the number of weight matrices examined. Unlike previous research, our statistic avoids the use of simulation to determine statistical significance in the presence of multiple testing. To test the validity of our approach, we constructed a numerical example to assess the statistic's performance and conducted an empirical study using leukemia data from central New York state. The developed statistic addresses the need for the empirical determination of weights and spatial scale. The test therefore addresses the common weakness of many applications, where weights are defined exogenously, with little or no thought given to either the definition or its implications. Los indicadores locales ( local spatial statistics) evalúan la asociación espacial de una o varias variables de interés dada un área predefinida y sus áreas vecinas. La mayoría de dichas medidas utilizan una escala única de análisis y prestan poca atención a la escala del proceso de generación de los datos. En los casos en los que el investigador no está seguro de la escala del proceso, las los indicadores locales pueden ser evaluados a varias escalas. En dichos casos, cuando se hace la evaluación de la significancia estadística de cada indicador local, es importante incorporar una corrección para pruebas múltiples ( multiple tests), un ajuste que raramente se realiza en la gran mayoría de estudios. Debido al problema de pruebas múltiples, los indicadores locales son más propensos a identificar relaciones significativas, incluso cuando no existe asociación espacial significativa alguna. En este artículo los autores desarrollan una metodología que produce un índice local de Moran que proporciona tanto una estimación empírica de la escala espacial de la asociación así como una evaluación de la importancia del indicador para dicha escala. La idea clave es poner a prueba una serie de opciones posibles para la definición de la matriz de pesos espaciales ( spatial weight matrix) del índice y luego tomar en cuenta las pruebas múltiples asociadas con el número de matrices de peso examinadas. A diferencia de métodos anteriores, el indicador local propuesto evita el uso de simulaciones para determinar la significancia estadística con pruebas múltiples. Para probar la validez del enfoque propuesto, se construyó un ejemplo numérico con el fin de evaluar el desempeño del nuevo índice y se llevó a cabo un estudio comparativo a partir de datos del centro de leucemia del estado de Nueva York. El índice desarrollado responde a la necesidad de definir las ponderaciones (pesos) empíricamente y la escala espacial. De esta forma el método propuesto supera limitaciones comúnmente halladas de muchas aplicaciones en las cuales los pesos son definidos exógenamente, con poca o ninguna atención a su definición o su implicancias. 局部空间统计量可用于度量和检验预定地理区域周围邻域的空间关联。大多数情况下仅采用单一尺度的分析而较少关注数据生成过程的尺度。而当其过程尺度无法确定时，局部统计量却可能检测出多个尺度。在这些案例中，对单个局部统计量统计显著性评估建立多重检验的修正是重要的，而这却鲜有实施。因此，即使存在无意义的空间关联时，局部统计也更可能识别出显著的相关性。 本文发展了一种基于局部Moran统计的方法，提供了空间尺度关联性的经验估计以及对该尺度下统计显著性的评估。其核心思想是测试统计权重矩阵的可能选择，然后考虑与权重矩阵检验数量数目相关的多重检验。与以往研究不同，该方法在多重检验情况中避免了采用模拟来确定统计显著性。为检验其有效性，采用了数值案例来评估其统计性能，并基于纽约州中部的血癌数据进行比较研究。该方法解决了权重和空间尺度确定经验估计的需求，通过验证也相应地解决了很多应用中的普遍弱点，即权重被定义成外生变量，而很少或根本没有考虑其定义或含义。 [ABSTRACT FROM AUTHOR]

Abstract: The present study aims to evaluate the field-based approach for the classification of landcover using high-resolution SAR data. TerraSAR-X (TSX) strip mode imagery, coupled with digital ortho-photos (DOPs) with 20cm spatial resolution was used for landcover classification and parcel mapping respectively. Different filtering and analysis techniques were applied to extract textural information from the TSX image in order to assess the enhancement of the classification accuracy. Several attributes of parcels were derived from the available TSX images in order to define the most suitable parameters discriminating between different landcover types. Then, these attributes were further statistically analysed in order to define separability and thresholds between different landcover types. The results showed that textural analysis resulted in high classification accuracy. Hence, this paper confirms that integrated landcover classification using the textural information of TerraSAR-X has a high potential for landcover mapping. [Copyright &y& Elsevier]

The article explores the possible role of entropy-based measures for detecting spatial structure. The possible role is partially based on the superior performance of dependence entropy measures over traditional measures and partially on the idea of symbolic entropy. A nonparametric statistical procedure for selecting the order of the spatial lag is provided, along with a proposed symbolization procedure.

We analyze the time evolution of an initial spatial coherence for a two level atom whose internal degrees of freedom interact with a single mode of a cavity field. When the qubit-field subsystem is taken as an environment, the translational dynamics experiences a decoherence process which may be encoded in a decoherence factor D. We find that the field statistics affects D through the alternative paths the system-environment may follow along their entanglement, while eventual field phase properties give rise to an imaginary part of D which is related to the atomic translation. From the decoherence perspective, we analyze the relation between the atomic momentum and the imaginary part of the atomic spatial density matrix, and some considerations on its asymptotic behavior are brought into question at the conclusion of the paper. [ABSTRACT FROM AUTHOR]

This article outlines the context in geography and statistics in the mid 1960s, at the height of geography's so-called “quantitative revolution,” that led us into a long-term collaboration about spatial statistics, which has continued in surges and lulls for some 40 years. We focus upon problems in spatial autocorrelation, including the measurement of autocorrelation, distribution theory, and variable geographical lattices. This narrative may not describe how it was, but it does describe how we remember the events of the time. [ABSTRACT FROM AUTHOR]

Model choice is one of the most crucial aspect in any statistical data analysis. It is well known that most models are just an approximation to the true data-generating process but among such model approximations, it is our goal to select the 'best' one. Researchers typically consider a finite number of plausible models in statistical applications, and the related statistical inference depends on the chosen model. Hence, model comparison is required to identify the 'best' model among several such candidate models. This article considers the problem of model selection for spatial data. The issue of model selection for spatial models has been addressed in the literature by the use of traditional information criteria-based methods, even though such criteria have been developed based on the assumption of independent observations. We evaluate the performance of some of the popular model selection critera via Monte Carlo simulation experiments using small to moderate samples. In particular, we compare the performance of some of the most popular information criteria such as Akaike information criterion (AIC), Bayesian information criterion, and corrected AIC in selecting the true model. The ability of these criteria to select the correct model is evaluated under several scenarios. This comparison is made using various spatial covariance models ranging from stationary isotropic to nonstationary models. [ABSTRACT FROM AUTHOR]

This paper proposes a novel feature-based invariant descriptor termed Radon composite features (RCFs) for planar shapes. Instead of analyzing shapes directly in the spatial domain, some shape features are extracted from the Radon transform plane using statistical and spectral analysis. The proposed method overcomes the drawbacks of existing shape representation techniques since it accomplishes the invariances to common geometrical transformations without any normalization process, which usually causes inaccuracies. A novel hierarchical strategy with RCFs can achieve low complexity and coarse-to-fine retrieval, and perform accurately when retrieving shapes, while remaining robust against variations. Experiments demonstrate that RCF provides a higher degree of discrimination as compared with several state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

The massive quantities of geographic information that are collected by modern sensing technologies are difficult to use and understand without data reduction methods that summarize distributions and report salient trends. Statistical analyses, therefore, are increasingly being used to analyze large geographic data sets over a broad spectrum of spatial and temporal scales. Computational Grids coordinate the use of distributed computational resources to form a large virtual supercomputer that can be applied to solve computationally intensive problems in science, engineering, and commerce. This paper presents a solution to computing a spatial statistic, Gi*(d) using Grids. Our approach is based on a quadtree-based domain decomposition that uses task-scheduling algorithms based on GridShell and Condor. Computational experiments carried out on the TeraGrid were designed to evaluate the performance of solution processes. The Grid-based approach to computing values for Gi*(d) shows improved performance over the sequential algorithm while also solving larger problem sizes. The solution demonstrated not only advances knowledge about the application of the Grid in spatial statistics applications but also provides insights into the design of Grid middleware for other computationally intensive applications. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Directional relation, as a kind of spatial constraints, has been recognized as being an important means for spatial query, analysis and reasoning. Directional relation is conventionally concerned with two point objects. However, in spatial query and analysis, there is also a need of directional relations between point and line, point and area, line and line, line and area, and area and area. Therefore, conventional definition of direction needs to be extended to include line and area objects (i.e. the so-called extended objects). Existing models for directional relation of extended objects make use of approximate representations (e.g. minimum bounding rectangles) of the extended objects so as to produce some results with unrealistic impression. In this paper, a statistical model is presented. In this new model, (1) an extended spatial object is decomposed into small components; (2) the directional relation between extended spatial objects is then determined by the directions between these small components which form a distribution; and (3) two measures (i.e. range and median direction) are utilized to describe the statistical property of the distribution. This statistical model is based upon the (extended) spatial objects themselves, instead of their approximate representations. An experimental test has been carried out and the result indicates that the directional relations computed from this model is very close to those perceived by human beings. [ABSTRACT FROM AUTHOR]

Abstract: Objective: In EEG/MEG experiments, increasing the number of sensors improves the spatial resolution of the results. However, the standard statistical methods are inappropriate for these multivariate, highly correlated datasets. We introduce a procedure to identify spatially extended scalp fields that correlate with some external, continuous measure (reaction-time, performance, clinical status) and to test their significance. Methods: We formally deduce that the channel-wise covariance of some experimental variable with scalp field data directly represents intracerebral sources associated with that variable. We furthermore show how the significance of such a representation can be tested with resampling techniques. Results: Simulations showed that depending on the number of channels and subjects, effects can be detected already at low signal to noise ratios. In a sample analysis of real data, we found that foreign-language evoked ERP data were significantly associated with foreign-language proficiency. Inverse solutions of the extracted covariances pointed to sources in language-related areas. Conclusions: Covariance mapping combined with bootstrapping methods has high statistical power and yields unique and directly interpretable results. Significance: The introduced methodology overcomes some of the ‘traditional’ statistical problems in EEG/MEG scalp data analysis. Its application can improve the reproducibility of results in the field of EEG/MEG. [Copyright &y& Elsevier]

Spatial statistics for very large spatial data sets is challenging. The size of the data set, n, causes problems in computing optimal spatial predictors such as kriging, since its computational cost is of order . In addition, a large data set is often defined on a large spatial domain, so the spatial process of interest typically exhibits non-stationary behaviour over that domain. A flexible family of non-stationary covariance functions is defined by using a set of basis functions that is fixed in number, which leads to a spatial prediction method that we call fixed rank kriging. Specifically, fixed rank kriging is kriging within this class of non-stationary covariance functions. It relies on computational simplifications when n is very large, for obtaining the spatial best linear unbiased predictor and its mean-squared prediction error for a hidden spatial process. A method based on minimizing a weighted Frobenius norm yields best estimators of the covariance function parameters, which are then substituted into the fixed rank kriging equations. The new methodology is applied to a very large data set of total column ozone data, observed over the entire globe, where n is of the order of hundreds of thousands. [ABSTRACT FROM AUTHOR]

The paper presents a novel method to design a spatial control system based on multirate output feedback robust sliding mode control for a large Pressurized Heavy Water Reactor (PHWR). The non-linear model of PHWR including xenon and iodine dynamics is characterized by 70 state variables and 14 inputs and outputs each. Linear nodal model is obtained by linearizing the non-linear dynamic equations of the reactor about the full power operating point. A multirate output feedback based discrete sliding mode spatial controller is designed for the linearized model of the reactor. The proposed control method does not require state information of the system for feedback purposes and hence may be easier to implement. From simulation of the non-linear model of the reactor in representative transients, the proposed control scheme is found to be superior to other methods. [ABSTRACT FROM AUTHOR]

Abstract: We propose in this Note an extension of Besag''s auto-models to exponential families with multi-dimensional parameters. This extension is necessary for the treatment of spatial models like the ones with Beta conditional distributions. A family of cooperative auto-models is proposed. To cite this article: C. Hardouin, J.-F. Yao, C. R. Acad. Sci. Paris, Ser. I 345 (2007). [Copyright &y& Elsevier]

Cross–scale interactions refer to processes at one spatial or temporal scale interacting with processes at another scale to result in nonlinear dynamics with thresholds. These interactions change the pattern–process relationships across scales such that fine-scale processes can influence a broad spatial extent or a long time period, or broad-scale drivers can interact with fine-scale processes to determine system dynamics. Cross–scale interactions are increasing recognized as having important influences on ecosystem processes, yet they pose formidable challenges for understanding and forecasting ecosystem dynamics. In this introduction to the special feature, “Cross–scale interactions and pattern–process relationships”, we provide a synthetic framework for understanding the causes and consequences of cross–scale interactions. Our framework focuses on the importance of transfer processes and spatial heterogeneity at intermediate scales in linking fine- and broad-scale patterns and processes. Transfer processes and spatial heterogeneity can either amplify or attenuate system response to broad-scale drivers. Providing a framework to explain cross–scale interactions is an important step in improving our understanding and ability to predict the impacts of propagating events and to ameliorate these impacts through proactive measures. [ABSTRACT FROM AUTHOR]

Variogram estimation plays an important role in many areas of spatial statistics. Potential areas of application include biology, ecology, economics and meteorology. However, it is common that, for example under highly correlated patterns, traditional estimators can not reflect all the spatial features or dependencies. In this paper, we present an alternative distribution-free estimator based on nearest-neighbour estimation with a non-constant smoothing field that is better able to adapt to spatially varying features of the data pattern. We present a simulation study to compare our new estimator to a nearest-neighbour estimator built with a constant smoothing parameter and to the classical variogram estimator. We apply our method to analyze two ecological data sets. [ABSTRACT FROM AUTHOR]

The past decade has witnessed extensive development of measures that examine characteristics of spatial subsets (local spaces) defined with respect to a complete data set (global space). Such procedures have evolved independently in fields such as geography, GIS, cartography, remote sensing, and landscape ecology. Collectively, we label these procedures as local spatial methods. We focus on those methods that share a common goal of identifying subsets whose characteristics are statistically 'significant' in some way. We propose the concept of local spatial statistical analysis (LoSSA) both as an integrative structure for existing methods and as a framework that facilitates the development of new local and global statistics. By formalizing what is involved when a particular local statistic is used, LoSSA helps to reveal the key features and limitations of the procedure. These include a consideration of the nature of the spatial subsets, their spatial relationship to the complete data set, and the relationship between a given global statistic and the corresponding local statistics computed for the data set. [ABSTRACT FROM AUTHOR]

The spatial Simon effect is often asymmetric, being greater on one side than on the other. To date, not much attention has been paid to these asymmetries, and explanations of the Simon effect do not take them into account. In the present article, we attempt to clarify the statistical implications of the asymmetries so as to provide a useful tool for future empirical investigation. Starting with examples from our laboratory and previous well-known studies, we point out the consequences of ignoring the asymmetries in the Simon effect. We suggest an alternative data analysis that might render the results clearer. Finally, through a comparison of left- and fight-handed subjects, we demonstrate that asymmetries in the Simon effect are linked to the lateralization of processes involved in the Simon task--that is, attention and response selection. This approach provides a strong argument against collapsing data from the two sides to measure the Simon effect. [ABSTRACT FROM AUTHOR]

Obtaining new and flexible classes of nonseparable spatio-temporal covariances and variograms has resulted a key point of research in the last years. The goal of this paper is to introduce and develop new spatio-temporal covariance models taking into account the problem of spatial anisotropy. Recent literature has focused on the problem of full symmetry and the problem of anisotropy has been overcome. Here we propose a generalization of Gneiting’s (J Am Stat Assoc 97:590–600, ) approach and obtain new classes of stationary nonseparable spatio-temporal covariance functions which are spatially anisotropic. The resulting structures are proved to have certain interesting mathematical properties, together with a considerable applicability. [ABSTRACT FROM AUTHOR]

In many applications, it is of interest to test whether a spatial point pattern is randomly generated after adjusting for an underlying spatial inhomogeneity. A great variety of different test statistics have been proposed for this purpose by scientists in different fields; these are reviewed in this article. Despite apparent dissimilarities in terms of their original formulations, most of these statistics can be placed into one general framework of which they are special cases. This makes it easier to see exactly how they relate to one another and also to determine which test to use for a particular application. The general framework can also be used for proposing new tests by combining properties of existing tests, for developing theoretical foundations for these types of test statistics, for doing structured comparative evaluations, and for software development. [ABSTRACT FROM AUTHOR]

In order to optimize the accuracy of the Nearest-Neighbor classification rule, a weighted distance is proposed, along with algorithms to automatically learn the corresponding weights. These weights may be specific for each class and feature, for each individual prototype, or for both. The learning algorithms are derived by (approximately) minimizing the Leaving-One-Out classification error of the given training set. The proposed approach is assessed through a series of experiments with UCI/STATLOG corpora, as well as with a more specific task of text classification which entails very sparse data representation and huge dimensionality. In all these experiments, the proposed approach shows a uniformly good behavior, with results comparable to or better than state-of-the-art results published with the same data so far. [ABSTRACT FROM AUTHOR]

Methods for map comparison such as the Kappa and Tau statistics have grown popular in applications of remote sensing accuracy assessment. These methods take pairs of raster maps as sets of paired observations and do not consider spatial structure except for cell-by-cell overlap. In contrast, landscape structure metrics such as mean patch size that are commonly used in landscape ecology do express spatial structure, however without addressing cell-by-cell overlap. This paper introduces a number of comparison methods that consider spatial structure and overlap simultaneously. They achieve this by involving the neighbourhood of a cell in the calculation of similarity at its location. For this, the methods make use of a distance weighted moving window. Two test cases demonstrate that the different comparison methods offer a spatial account of varied aspects of map similarity. It is found that the methods can best be used in conjunction with a visual analysis; they then serve to quantify, reject or confirm hypotheses. [ABSTRACT FROM AUTHOR]

Spatial joins find all pairs of objects that satisfy a given spatial relationship. In spatial joins using indexes, original-space indexes such as the R-tree are widely used. An original-space index is the one that indexes objects as represented in the original space. Since original-space indexes deal with extents of objects, it is relatively complex to optimize join algorithms using these indexes. On the other hand, transform-space indexes, which transform objects in the original space into points in the transform space and index them, deal only with points but no extents. Thus, optimization of join algorithms using these indexes can be relatively simple. However, the disadvantage of these join algorithms is that they cannot be applied to original-space indexes such as the A-tree. In this paper, we present a novel mechanism for achieving the best of these two types of algorithms. Specifically, we propose the new notion of the transform-space view and present the transform-space viewjoin algorithm. The transform-space view is a virtual transform-space index based on an original-space index. It allows us to "interpret" or "view" an existing original-space index as a transform-space index with no space and negligible time overhead and without actually modifying the structure of the original-space index or changing object representation. The transform-space view join algorithm joins two original-space indexes in the transform space through the notion of the transform-space view. Through analysis and experiments, we verity the excellence of the transform-space view join algorithm. The transform-space view join algorithm always outperforms existing ones for all the data sets tested in terms of all three measures used: the one-pass buffer size (the minimum buffer size required for guaranteeing one disk access per page), the number of disk accesses for a given buffer size, and the wall clock time. Thus, it constitutes a lower-bound algorithm. We believe that the proposed transform-space view can be applied to developing various new spatial query processing algorithms in the transform space. [ABSTRACT FROM AUTHOR]

The ability to detect anomalies such as spatial clustering in data sets plays an important role in spatial data analysis, leading to interest in test statistics identifying patterns exhibiting significant levels of clustering. Toward this end, Tango (1995) proposed a statistic (and its associated distribution under a null hypothesis of no clustering) assessing overall patterns of spatial clustering in a set of observed regional counts. Rogerson (1999) observed that Tango's index may be decomposed into the summation of two distinct statistics, the first mirroring standard tests of goodness-of-fit (GOF), and the second an index of spatial association (SA) similar to Moran's I. In this article, we investigate the effectiveness of Rogerson's expression of Tango's statistic in separating GOF from SA in data sets containing clusters. We simulate data under the null hypothesis of no clustering as well as two alternative hypotheses. The first alternative hypothesis induces a poor fit from the null hypothesis while maintaining independent observations and the second alternative hypothesis induces spatial dependence while maintaining fit. Using Rogerson's decomposition and leukemia incidence data from upstate New York, we show graphically that one is unable to statistically distinguish poor fit from autocorrelation. [ABSTRACT FROM AUTHOR]

Statistical models for spot shapes and signal intensities are used in image analysis of laser scans of microarrays. Most models have essentially been based on the assumption of independent pixel intensity values, but models that allow for spatial correlation among neighboring pixels can accommodate errors in the microarray slide and should improve the model fit. Five spatial correlation structures, exponential, Gaussian, linear, rational quadratic and spherical, are compared for a dataset with 50-mer two-colour oligonucleotide microarrays and 452 probes for selected Arabidopsis genes. Substantial improvement in model fit is obtained for all five correlation structures compared to the model with independent pixel values, and the Gaussian and the spherical models seem to be slightly better than the other three models. We also conclude that for the data set analysed the correlation seems negligible for non-neighboring pixels. [ABSTRACT FROM AUTHOR]

A common requirement for spatial modeling is the development of an appropriate correlation structure. Although the assumption of isotropy is often made for this structure, it is not always appropriate. A conventional practice when checking for isotropy is to informally assess plots of direction-specific sample (semi) variograms. Although a useful diagnostic, these graphical techniques are difficult to assess and open to interpretation. Formal alternatives to graphical diagnostics are valuable, but have been applied to a limited class of models. In this article we propose a formal approach to test for isotropy that is both objective and valid for a wide class of models. This approach, which is based on the asymptotic joint normality of the sample variogram, can be used to compare sample variograms in multiple directions. An L2- consistent subsampling estimator for the asymptotic covariance matrix of the sample variogram is derived and used to construct a test statistic. A subsampling approach and a limiting chi-squared approach are developed to obtain p values of the test. Our testing approach is purely nonparametric in that no explicit knowledge of the marginal or joint distribution of the process is needed. In addition, the shape of the random field can be quite irregular. The results apply to regularly spaced data as well as to irregularly spaced data when the point locations are generated by a homogeneous Poisson process. A data example and simulation experiments demonstrate the efficacy of the approach. [ABSTRACT FROM AUTHOR]

Statistical inference is important for all those who engage in the analysis of spatial data. The issue is becoming increasingly important given the explosion in the availability of spatial data and the proliferation of Geographic Information Systems (GIS) across different academic disciplines and application areas. The aim of this paper is to provide a brief overview of some of the concepts and controversies inherent in statistical inference in the hope of raising the level of awareness within the geographic information science community that different points of view exist when it comes to inference. We argue that the concept of statistical inference in spatial data analysis and spatial modelling is perhaps broader than many GIS users imagine. In particular, we argue that different types of inference exist and that process inference is just as valid as sample inference, even though the latter appears to dominate the GIS literature. [ABSTRACT FROM AUTHOR]

Network systems evolving by preferential attachment of new vertices and by link loading are considered. The probability of node attaching is assumed to depend linearly on degrees of existing nodes to which new ones are connected. The rule of the network loading allows both deterministic and random processes of distributing weights among links. Specifically, the rule is determined by assigning to each link a weight dependent on randomly modified intervals between times at which linked vertices are connected to the system. This enables the investigation of the influence of local and global loading processes on statistical properties of weighted networks. It is demonstrated that, for different values of parameters controlling these processes, the distribution of weights concentrated at vertices of such networks displays a large variety of scale-free and truncated scale-free behaviors. It is also shown that statistical properties of the studied weighted networks and statistical properties of some complex evolving spatial systems exhibit a close relationship. [Copyright &y& Elsevier]

Likelihood methods are often difficult to use with large, irregularly sited spatial data sets, owing to the computational burden. Even for Gaussian models, exact calculations of the likelihood for n observations require O( n3) operations. Since any joint density can be written as a product of conditional densities based on some ordering of the observations, one way to lessen the computations is to condition on only some of the ‘past’ observations when computing the conditional densities. We show how this approach can be adapted to approximate the restricted likelihood and we demonstrate how an estimating equations approach allows us to judge the efficacy of the resulting approximation. Previous work has suggested conditioning on those past observations that are closest to the observation whose conditional density we are approximating. Through theoretical, numerical and practical examples, we show that there can often be considerable benefit in conditioning on some distant observations as well. [ABSTRACT FROM AUTHOR]

Presents a method, called the snake skeleton graph, for analyzing the sensor signals that contain spatial information. Utilization of the Be´zier surface as a model for spatial information of the signals; Description on the construction of snake skeleton graph; Presentation of an application for fault diagnosis in sheet metal stamping operation; Discussion of future research topics.

This paper describes a procedure for extending local statistics to categorical spatial data. The approach is based on the notion that there are two fundamental characteristics of categorical spatial data; composition and configuration. Further, it is argued that, when considered locally, the latter should be measured conditionally with respect to the former. These ideas are developed for binary, gridded data. Local composition is measured by counting the numbers of cells of a particular type, while local configuration is measured by join counts. The approach is illustrated using a small, empirical data set and an ad hoc procedure is developed to deal with the impact of global spatial autocorrelation on the local statistics. [ABSTRACT FROM AUTHOR]

Summary The major aim of crop variety evaluation is to predict the future performance of varieties. This paper presents the routine statistical analysis of data from late-stage testing of crop varieties in Australia. It uses a two-stage approach for analysis. The data from individual trials from the current year are analysed using spatial techniques. The resultant table of variety-by-trial means is combined with tables from previous years to form the data for an overall mixed model analysis. Weights allow for the data being estimates with varying accuracy. In view of the predictive aim of the analysis, variety effects and interactions are regarded as random effects. Appropriate inferential tools have been developed to assist with interpretation of the results. Analyses must be conducted in a timely manner so that variety predictions can be published and disseminated to growers immediately after harvest each year. Factors which facilitate this include easy access to historic data and the use of specialist mixed model software. [ABSTRACT FROM AUTHOR]

In spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations; in other words, the data form a realization of a marked point process. In this paper, we formulate subsampling estimators of the moments of general statistics computed from marked point process data, and we establish their L [sub 2] -consistency. The variance estimator in particular can be used for the construction of confidence intervals for estimated parameters. A practical data-based method for choosing a subsampling parameter is given and illustrated on a data set. Finite sample simulation examples are also presented. [ABSTRACT FROM AUTHOR]

A traditional method of summarizing spatial distribution of species is the observed species-area curve. Often the observed species-area curve is surprisingly close to the expected species-area curve under the hypothesis of random placement of individuals. This has been used as evidence supporting the hypothesis. In this paper, we argue that using the observed species-area curve to test the general random placement hypothesis is highly inefficient. We present a testing method based on the classical $\backslash chi^\{2\}$ test for over-dispersion which is not only more efficient but also applicable to situations where complete abundance information are unavailable. We also discuss three alternatives of the hypothesis. The focus of this paper is on these and other general issues relevant to communities of different types. No applications are included in this paper. [ABSTRACT FROM AUTHOR]

Two statistical methods to reconstruct the spatial pattern of environmental data are compared: the Kriging and the Bilinear. The comparison is performed by evaluating two different characteristics of the methods: the interpolation and the estimation. The Kriging method is demonstrated to be better than the Bilinear regarding all the statistics studied, although the differences are not very significant. Especially, the Kriging is more efficient than the Bilinear in the reconstruction of peak values and it does not extrapolate local trends. The methods are applied to a set of environmental data measured in an urban area. [ABSTRACT FROM AUTHOR]

The Hypercarte Project, a research network established in 1996, has proposed a general solution to this problem. This solution is based on the concept of multiscalar spatial neighbourhood, with a particular insight to the case of gaussian neighbourhood which presents interesting theoretical and empirical properties for the analysis of the distribution of social and economic distributions. In a first part, the paper presents a detailed description of the mathematical basis of this method on a theoretical example. In a second part, the political consequences of the method are analysed through a classical problem of territorial planning. [ABSTRACT FROM AUTHOR]

Presents a study which derived the extended spatial decorrelation method that uses second-order statistics in space for separating intrinsic signals. Use of optical imaging of intrinsic signals; Data structure of optical recordings; Summary and conclusion.

The application of spatial econometrics techniques to microlevel data of firms or households is problematic because of potentially large sample sizes and more-complicated spatial weight matrices. This paper provides the first application to actual household-level data of a new generalized-moments (GM) estimation technique developed by Kelejian and Prucha. The results based on this method, which is computationally feasible for any size data set, track those generated from the more conventional maximum-likelihood approach. The GM approach is shown to have the added advantage of easily allowing estimation of a more flexible functional form for the spatial weight matrix. [ABSTRACT FROM AUTHOR]

This article reports the results of an experimental study of the three firm location problem. We compare the subjects' behavior in the experiments with the symmetric mixed strategy Nash equilibrium calculated by Shaked. Overall, the findings are consistent with the equilibrium prediction. However, the subjects' locations were significantly more dispersed than predicted by the theory. Three alternative explanations of this phenomenon--inexperience, approximate equilibrium behavior and risk aversion--are suggested and evaluated for their predictive power. Special attention is paid to risk aversion. (JEL C9, C72, D43) [ABSTRACT FROM AUTHOR]

This article sought to present a process of abrupt transition where technological innovation is concerned. The matter taken up in particular was accelerating digitalisation, in the wider context of digital transformation, and in this case, in reference to spatial planning issues. This article offers an assessment of the level of digitalisation and digital transformation of spatial planning, with this, in turn, making it possible to define the potential at the disposal of rural areas, as they seek to bring in the idea of smart rural development. The empirical analyses present herein are founded upon secondary statistical data as well as our own primary data on the subject of geoportals and their functionality in rural parts of the Łódź region (Poland). The assessments of both planning coverage and geoportal functionality reported herein provide insight regarding the potential for rural areas to implement the concept of GeoDesign, as an integral part of "smart rural development". The research carried out made it clear that only a fifth of rural gminas in the region are of high potential where GeoDesign is concerned, while every third gmina has only very low potential. A further key conclusion is that rural gminas heading along the path of "smart development" may break out of a spatial order existing thus far on the basis of disparities, and a division of regions into a centre and peripheries. This is of major significance in the context of the diffusion of innovation that digitalisation and digital transformation represent. [ABSTRACT FROM AUTHOR]

Focuses on a study which extended the ideas of the well-known Swendsen-Wang-Wolff cluster algorithms in statistical physics to build algorithms for simulating spatial point processes. Cluster algorithms for pairwise interactions; Convergence of the algorithms; Generalizations.

Abstract. This paper develops statistical methods for analyzing the distribution of spatial objects points, convex polygons, and line segments in relation to a surface. We propose statistics for measuring the relationship between the distribution of these objects and a surface and derive their expectations and variances under the null hypothesis that the objects are independently and randomly distributed. The statistics are approximately distributed according to the normal distribution under the null hypothesis, which enables us to test the significance of the spatial relationships statistically. Using the proposed methods, we empirically analyze the distribution of convenience stores in relation to the distribution of population in a suburb of Osaka, Japan. Some empirical findings are shown. [ABSTRACT FROM AUTHOR]

This article presents two indirect tests of the spatial mismatch hypothesis. A wage-gradient model and a two-sample t-test procedure are used to examine wage differences across the Cleveland primary metropolitan statistical area (PMSA) for 18 selected low-wage industries. Empirical evidence produced in both sets of tests do not support the spatial mismatch hypothesis in the context of the Cleveland PMSA: A positive wage gradient was not found, and two-sample t-tests did not indicate that wages in industries typified as being predominantly low skilled are higher in suburbs than in the central city — an outcome predicted by a spatial mismatch — for all industries in the sample, with the exception of gasoline service stations. [ABSTRACT FROM AUTHOR]

Presents a study which examined spatial statistical analysis of aggregate voting returns, in Nazi Party, Germany. How the growth of the Nazi Party vote in Baden between May 1924 and July 1932; Use of spatial heterogeneity in the Nazi Party's electorate; Importance of geography in helping to explain the nature of the Nazi Party vote.

Presents an extension on the construction of higher-order spatial lag operators, done by Blommestein and Koper (1992). Graphic theoretics on spatial lag operators; Data structures for storage; Algorithms; Efficiency of algorithms designed.

Presents a numerical model for the study of spatial structures consisting of curved, three-dimensional members with variable cross sections. Analysis of the ultimate capacity of masonry arches and frames; Proposed treatment of masonry arches and frames; Flexibility-based analysis of masonry frames with curved members.

Abstract Conceptual and logistical challenges associated with the design and analysis of ecological restoration experiments are often viewed as being insurmountable, thereby limiting the potential value of restoration experiments as tests of ecological theory. Such research constraints are, however, not unique within the environmental sciences. Numerous natural and anthropogenic disturbances represent unplanned, uncontrollable events that cannot be replicated or studied using traditional experimental approaches and statistical analyses. A broad mix of appropriate research approaches (e.g., long-term studies, large-scale comparative studies, space-for-time substitution, modeling, and focused experimentation) and analytical tools (e.g., observational, spatial, and temporal statistics) are available and required to advance restoration ecology as a scientific discipline. In this article, research design and analytical options are described and assessed in relation to their applicability to restoration ecology. Significant research benefits may be derived from explicitly defining conceptual models and presuppositions, developing multiple working hypotheses, and developing and archiving high-quality data and metadata. Flexibility in research approaches and statistical analyses, high-quality databases, and new sampling approaches that support research at broader spatial and temporal scales are critical for enhancing ecological understanding and supporting further development of restoration ecology as a scientific discipline. [ABSTRACT FROM AUTHOR]