# 空间统计学

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**Spatial analysis** or **spatial statistics** includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is the technique applied to structures at the human scale, most notably in the analysis of geographic data or transcriptomics data.

Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is the technique applied to structures at the human scale, most notably in the analysis of geographic data or transcriptomics data.

空间分析或空间统计包括任何形式的技术，研究实体使用他们的拓扑，几何，或地理属性。空间分析包括各种技术，其中许多技术仍处于早期发展阶段，使用不同的分析方法，应用于天文学等各种领域，研究宇宙中星系的位置，利用”位置和路线”算法建造复杂的布线结构，进行芯片制造工程。在更加有限的意义上，空间分析是在人类尺度上应用于结构的技术，尤其是在地理数据或转录组数据的分析中。

Complex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research. The most fundamental of these is the problem of defining the spatial location of the entities being studied.

Complex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research. The most fundamental of these is the problem of defining the spatial location of the entities being studied.

在空间分析中出现了一些复杂的问题，其中许多问题既没有明确界定，也没有完全解决，但却构成了当前研究的基础。其中最基本的问题是确定所研究实体的空间位置。

Classification of the techniques of spatial analysis is difficult because of the large number of different fields of research involved, the different fundamental approaches which can be chosen, and the many forms the data can take.

Classification of the techniques of spatial analysis is difficult because of the large number of different fields of research involved, the different fundamental approaches which can be chosen, and the many forms the data can take.

空间分析技术的分类是一个难点，因为涉及的研究领域很多，可以选择的基本方法也不同，而且数据可以采取多种形式。

## History

Spatial analysis began with early attempts at cartography and surveying. Land surveying goes back to at least 1,400 B.C in Egypt: the dimensions of taxable land plots were measured with measuring ropes and plumb bobs.^{[1]} b. Many fields have contributed to its rise in modern form. Biology contributed through botanical studies of global plant distributions and local plant locations, ethological studies of animal movement, landscape ecological studies of vegetation blocks, ecological studies of spatial population dynamics, and the study of biogeography. Epidemiology contributed with early work on disease mapping, notably John Snow's work of mapping an outbreak of cholera, with research on mapping the spread of disease and with location studies for health care delivery. Statistics has contributed greatly through work in spatial statistics. Economics has contributed notably through spatial econometrics. Geographic information system is currently a major contributor due to the importance of geographic software in the modern analytic toolbox. Remote sensing has contributed extensively in morphometric and clustering analysis. Computer science has contributed extensively through the study of algorithms, notably in computational geometry. Mathematics continues to provide the fundamental tools for analysis and to reveal the complexity of the spatial realm, for example, with recent work on fractals and scale invariance. Scientific modelling provides a useful framework for new approaches.模板:Cn

Spatial analysis began with early attempts at cartography and surveying. Land surveying goes back to at least 1,400 B.C in Egypt: the dimensions of taxable land plots were measured with measuring ropes and plumb bobs.The History of Land Surveying. Accessed Dec 17 2020. https://info.courthousedirect.com/blog/history-of-land-surveying b. Many fields have contributed to its rise in modern form. Biology contributed through botanical studies of global plant distributions and local plant locations, ethological studies of animal movement, landscape ecological studies of vegetation blocks, ecological studies of spatial population dynamics, and the study of biogeography. Epidemiology contributed with early work on disease mapping, notably John Snow's work of mapping an outbreak of cholera, with research on mapping the spread of disease and with location studies for health care delivery. Statistics has contributed greatly through work in spatial statistics. Economics has contributed notably through spatial econometrics. Geographic information system is currently a major contributor due to the importance of geographic software in the modern analytic toolbox. Remote sensing has contributed extensively in morphometric and clustering analysis. Computer science has contributed extensively through the study of algorithms, notably in computational geometry. Mathematics continues to provide the fundamental tools for analysis and to reveal the complexity of the spatial realm, for example, with recent work on fractals and scale invariance. Scientific modelling provides a useful framework for new approaches.

空间分析始于早期地图绘制和测量的尝试。土地测量至少可以追溯到公元前1400年的埃及: 应税地块的尺寸是用测量绳和铅锤测量的。土地测量的历史。2020. archdaily. Accessed Dec 172020. https://info.courthousedirect.com/blog/history-of-land-surveying.许多领域促成了它的现代形式的崛起。通过对全球植物分布和当地植物位置的植物学研究、动物运动的行为学研究、植被块的景观生态学研究、空间族群动态的生态学研究和生物地理学研究，生物学做出了贡献。流行病学对疾病地图绘制的早期工作做出了贡献，特别是约翰 · 斯诺绘制霍乱疫情地图的工作，绘制疾病传播地图的研究，以及提供保健服务的地点研究。统计工作通过空间统计工作作出了重大贡献。经济学通过空间计量经济学作出了显著的贡献。由于地理软件在现代分析工具箱中的重要性，地理信息系统目前是一个主要贡献者。遥感技术在形态学和聚类分析方面有着广泛的应用。计算机科学通过对算法的研究做出了广泛的贡献，尤其是在计算几何。数学继续为分析和揭示空间领域的复杂性提供基础工具，例如，最近的分形和尺度不变性。科学模型为新方法提供了一个有用的框架。

## Fundamental issues

Spatial analysis confronts many fundamental issues in the definition of its objects of study, in the construction of the analytic operations to be used, in the use of computers for analysis, in the limitations and particularities of the analyses which are known, and in the presentation of analytic results. Many of these issues are active subjects of modern research.模板:Cn

Spatial analysis confronts many fundamental issues in the definition of its objects of study, in the construction of the analytic operations to be used, in the use of computers for analysis, in the limitations and particularities of the analyses which are known, and in the presentation of analytic results. Many of these issues are active subjects of modern research.

基本问题空间分析在其研究对象的定义、将要使用的分析操作的构造、用于分析的计算机、已知的分析的局限性和特殊性以及分析结果的表示等方面面临许多基本问题。其中许多问题是现代研究的活跃课题。

Common errors often arise in spatial analysis, some due to the mathematics of space, some due to the particular ways data are presented spatially, some due to the tools which are available. Census data, because it protects individual privacy by aggregating data into local units, raises a number of statistical issues. The fractal nature of coastline makes precise measurements of its length difficult if not impossible. A computer software fitting straight lines to the curve of a coastline, can easily calculate the lengths of the lines which it defines. However these straight lines may have no inherent meaning in the real world, as was shown for the coastline of Britain.模板:Cn

Common errors often arise in spatial analysis, some due to the mathematics of space, some due to the particular ways data are presented spatially, some due to the tools which are available. Census data, because it protects individual privacy by aggregating data into local units, raises a number of statistical issues. The fractal nature of coastline makes precise measurements of its length difficult if not impossible. A computer software fitting straight lines to the curve of a coastline, can easily calculate the lengths of the lines which it defines. However these straight lines may have no inherent meaning in the real world, as was shown for the coastline of Britain.

空间分析中经常出现常见的错误，有些是由于空间的数学问题，有些是由于数据以空间方式呈现的特殊方式，有些是由于现有的工具。由于人口普查数据通过将数据聚合到地方单位来保护个人隐私，因此引发了一系列统计问题。海岸线的分形特性使得精确测量海岸线的长度变得困难，如果不是不可能的话。一个计算机软件拟合一条海岸线曲线的直线，可以很容易地计算出它所定义的直线的长度。然而，这些直线在现实世界中可能没有内在的含义，正如英国海岸线所显示的那样。

These problems represent a challenge in spatial analysis because of the power of maps as media of presentation. When results are presented as maps, the presentation combines spatial data which are generally accurate with analytic results which may be inaccurate, leading to an impression that analytic results are more accurate than the data would indicate.^{[2]}

These problems represent a challenge in spatial analysis because of the power of maps as media of presentation. When results are presented as maps, the presentation combines spatial data which are generally accurate with analytic results which may be inaccurate, leading to an impression that analytic results are more accurate than the data would indicate.Mark Monmonier How to Lie with Maps University of Chicago Press, 1996.

这些问题代表了空间分析的挑战，因为地图作为表达媒介的力量。当结果以地图形式提出时，表述方式将通常准确的空间数据与可能不准确的分析结果结合起来，导致分析结果比数据表明的更准确的印象。如何躺在地图上芝加哥大学出版社，1996年。

### Spatial characterization

The definition of the spatial presence of an entity constrains the possible analysis which can be applied to that entity and influences the final conclusions that can be reached. While this property is fundamentally true of all analysis, it is particularly important in spatial analysis because the tools to define and study entities favor specific characterizations of the entities being studied. Statistical techniques favor the spatial definition of objects as points because there are very few statistical techniques which operate directly on line, area, or volume elements. Computer tools favor the spatial definition of objects as homogeneous and separate elements because of the limited number of database elements and computational structures available, and the ease with which these primitive structures can be created.模板:Cn

thumb|240px|Spread of bubonic plague in medieval Europe. The colors indicate the spatial distribution of plague outbreaks over time.The definition of the spatial presence of an entity constrains the possible analysis which can be applied to that entity and influences the final conclusions that can be reached. While this property is fundamentally true of all analysis, it is particularly important in spatial analysis because the tools to define and study entities favor specific characterizations of the entities being studied. Statistical techniques favor the spatial definition of objects as points because there are very few statistical techniques which operate directly on line, area, or volume elements. Computer tools favor the spatial definition of objects as homogeneous and separate elements because of the limited number of database elements and computational structures available, and the ease with which these primitive structures can be created.

中世纪欧洲黑死病的传播角色塑造。这些颜色显示了随着时间的推移鼠疫爆发的空间分布。一个实体的空间存在的定义限制了可以适用于该实体的可能分析，并影响到可以得出的最终结论。虽然这个性质在所有分析中都是基本正确的，但在空间分析中尤其重要，因为定义和研究实体的工具有利于被研究实体的特定描述。统计技术倾向于将对象的空间定义为点，因为很少有统计技术直接在线、面积或体元素上进行操作。由于可用的数据库元素和计算结构的数量有限，而且这些基本结构可以轻松创建，因此计算机工具倾向于将对象的空间定义为同构和单独的元素。

### Spatial dependence

### Spatial dependence

# = = 空间依赖 = =

**Spatial dependence** is the spatial relationship of variable values (for themes defined over space, such as rainfall) or locations (for themes defined as objects, such as cities). Spatial dependence is measured as the existence of statistical dependence in a collection of random variables, each of which is associated with a different geographical location. Spatial dependence is of importance in applications where it is reasonable to postulate the existence of corresponding set of random variables at locations that have not been included in a sample. Thus rainfall may be measured at a set of rain gauge locations, and such measurements can be considered as outcomes of random variables, but rainfall clearly occurs at other locations and would again be random. Because rainfall exhibits properties of autocorrelation, spatial interpolation techniques can be used to estimate rainfall amounts at locations near measured locations.^{[3]}

Spatial dependence is the spatial relationship of variable values (for themes defined over space, such as rainfall) or locations (for themes defined as objects, such as cities). Spatial dependence is measured as the existence of statistical dependence in a collection of random variables, each of which is associated with a different geographical location. Spatial dependence is of importance in applications where it is reasonable to postulate the existence of corresponding set of random variables at locations that have not been included in a sample. Thus rainfall may be measured at a set of rain gauge locations, and such measurements can be considered as outcomes of random variables, but rainfall clearly occurs at other locations and would again be random. Because rainfall exhibits properties of autocorrelation, spatial interpolation techniques can be used to estimate rainfall amounts at locations near measured locations.Journel, A G and Huijbregts, C J, Mining Geostatistics, Academic Press Inc, London.

空间依赖性是可变值(对于在空间上定义的主题，如降雨)或位置(对于定义为对象的主题，如城市)之间的空间关系。空间相关性是指在一组随机变量中存在统计相关性，每个随机变量都与不同的地理位置有关。空间依赖在应用中非常重要，因为可以合理地假定在未包括在样本中的位置存在相应的一组随机变量。因此，降雨量可以在一组雨量计位置进行测量，这样的测量可以被认为是随机变量的结果，但是降雨明显发生在其他地点，而且也是随机的。由于降雨具有自相关特性，空间插值技术可用于估计测量点附近的降雨量。《矿业地质统计学》 ，英国伦敦学术出版社。

As with other types of statistical dependence, the presence of spatial dependence generally leads to estimates of an average value from a sample being less accurate than had the samples been independent, although if negative dependence exists a sample average can be better than in the independent case. A different problem than that of estimating an overall average is that of spatial interpolation: here the problem is to estimate the unobserved random outcomes of variables at locations intermediate to places where measurements are made, on that there is spatial dependence between the observed and unobserved random variables.模板:Cn

As with other types of statistical dependence, the presence of spatial dependence generally leads to estimates of an average value from a sample being less accurate than had the samples been independent, although if negative dependence exists a sample average can be better than in the independent case. A different problem than that of estimating an overall average is that of spatial interpolation: here the problem is to estimate the unobserved random outcomes of variables at locations intermediate to places where measurements are made, on that there is spatial dependence between the observed and unobserved random variables.

与其他类型的统计依赖一样，空间依赖的存在通常导致样本的平均值估计数不如独立样本的估计数准确，尽管如果存在负依赖，样本平均值可能比独立样本的估计数更准确。与估计总体平均值不同的一个问题是空间内插问题: 这里的问题是估计观测和未观测随机变量之间存在空间依赖关系的中间地点的未观测随机变量的结果。

Tools for exploring spatial dependence include: spatial correlation, spatial covariance functions and semivariograms. Methods for spatial interpolation include Kriging, which is a type of best linear unbiased prediction. The topic of spatial dependence is of importance to geostatistics and spatial analysis.模板:Cn

Tools for exploring spatial dependence include: spatial correlation, spatial covariance functions and semivariograms. Methods for spatial interpolation include Kriging, which is a type of best linear unbiased prediction. The topic of spatial dependence is of importance to geostatistics and spatial analysis.

探索空间相关性的工具包括: 空间相关性、空间协方差函数和半方差图。空间插值的方法包括克里格法，这是最佳线性无偏预测的一种。空间相关性是地质统计学和空间分析的重要课题。

#### Spatial auto-correlation

Spatial dependency is the co-variation of properties within geographic space: characteristics at proximal locations appear to be correlated, either positively or negatively. Spatial dependency leads to the **spatial autocorrelation** problem in statistics since, like temporal autocorrelation, this violates standard statistical techniques that assume independence among observations. For example, regression analyses that do not compensate for spatial dependency can have unstable parameter estimates and yield unreliable significance tests. Spatial regression models (see below) capture these relationships and do not suffer from these weaknesses. It is also appropriate to view spatial dependency as a source of information rather than something to be corrected.^{[4]}

Spatial dependency is the co-variation of properties within geographic space: characteristics at proximal locations appear to be correlated, either positively or negatively. Spatial dependency leads to the spatial autocorrelation problem in statistics since, like temporal autocorrelation, this violates standard statistical techniques that assume independence among observations. For example, regression analyses that do not compensate for spatial dependency can have unstable parameter estimates and yield unreliable significance tests. Spatial regression models (see below) capture these relationships and do not suffer from these weaknesses. It is also appropriate to view spatial dependency as a source of information rather than something to be corrected.

= = = = 空间自相关 = = = = 空间依赖性是地理空间内属性的共同变化: 近端位置的特征似乎是正相关或负相关的。空间依赖导致了统计学中的空间自相关问题，因为像时间自相关一样，这违反了假定观察值之间独立的标准统计技术。例如，不补偿空间相关性的回归分析可能具有不稳定的参数估计和产生不可靠的显著性检验。空间回归模型(见下文)捕获了这些关系，并且没有受到这些弱点的影响。将空间依赖性视为信息来源而不是需要纠正的东西也是适当的。

Locational effects also manifest as spatial heterogeneity, or the apparent variation in a process with respect to location in geographic space. Unless a space is uniform and boundless, every location will have some degree of uniqueness relative to the other locations. This affects the spatial dependency relations and therefore the spatial process. Spatial heterogeneity means that overall parameters estimated for the entire system may not adequately describe the process at any given location.模板:Cn

Locational effects also manifest as spatial heterogeneity, or the apparent variation in a process with respect to location in geographic space. Unless a space is uniform and boundless, every location will have some degree of uniqueness relative to the other locations. This affects the spatial dependency relations and therefore the spatial process. Spatial heterogeneity means that overall parameters estimated for the entire system may not adequately describe the process at any given location.

位置效应还表现为空间异质性，或者是地理空间中位置的明显变化。除非一个空间是均匀的和无限的，否则每个位置相对于其他位置都会有一定程度的独特性。这会影响空间依赖关系，从而影响空间过程。空间异质性意味着为整个系统估计的总体参数可能不足以描述任何给定位置的过程。

### Spatial association

**Spatial association** is the degree to which things are similarly arranged in space. Analysis of the distribution patterns of two phenomena is done by map overlay. If the distributions are similar, then the spatial association is strong, and vice versa.^{[5]} In a Geographic Information System, the analysis can be done quantitatively. For example, a set of observations (as points or extracted from raster cells) at matching locations can be intersected and examined by regression analysis.

Spatial association is the degree to which things are similarly arranged in space. Analysis of the distribution patterns of two phenomena is done by map overlay. If the distributions are similar, then the spatial association is strong, and vice versa. In a Geographic Information System, the analysis can be done quantitatively. For example, a set of observations (as points or extracted from raster cells) at matching locations can be intersected and examined by regression analysis.

空间联想是事物在空间中类似排列的程度。利用地图叠加技术对两种现象的分布模式进行了分析。如果分布相似，那么空间关联性就很强，反之亦然。在地理信息系统中，可以进行定量分析。例如，在匹配位置的一组观察值(作为点或者从光栅细胞中提取)可以被回归分析分割和检查。

Like spatial autocorrelation, this can be a useful tool for spatial prediction. In spatial modeling, the concept of spatial association allows the use of covariates in a regression equation to predict the geographic field and thus produce a map.

Like spatial autocorrelation, this can be a useful tool for spatial prediction. In spatial modeling, the concept of spatial association allows the use of covariates in a regression equation to predict the geographic field and thus produce a map.

与空间自相关一样，这可以成为空间预测的有用工具。在空间建模中，空间关联的概念允许使用回归方程中的协变量来预测地理场，从而生成地图。

### Scaling

Spatial measurement scale is a persistent issue in spatial analysis; more detail is available at the modifiable areal unit problem (MAUP) topic entry. Landscape ecologists developed a series of scale invariant metrics for aspects of ecology that are fractal in nature.^{[6]} In more general terms, no scale independent method of analysis is widely agreed upon for spatial statistics.模板:Cn

Spatial measurement scale is a persistent issue in spatial analysis; more detail is available at the modifiable areal unit problem (MAUP) topic entry. Landscape ecologists developed a series of scale invariant metrics for aspects of ecology that are fractal in nature. In more general terms, no scale independent method of analysis is widely agreed upon for spatial statistics.

= = = 缩放 = = = 空间测量尺度是空间分析中一个长期存在的问题，更多的细节可以在可调整地区单元问题的主题条目中找到。景观生态学家为自然界的分形生态学研究开发了一系列尺度不变量度。在更一般的条件下，没有规模独立的分析方法是广泛认同的空间统计学。

### Sampling

Spatial sampling involves determining a limited number of locations in geographic space for faithfully measuring phenomena that are subject to dependency and heterogeneity.^{[citation needed]} Dependency suggests that since one location can predict the value of another location, we do not need observations in both places. But heterogeneity suggests that this relation can change across space, and therefore we cannot trust an observed degree of dependency beyond a region that may be small. Basic spatial sampling schemes include random, clustered and systematic. These basic schemes can be applied at multiple levels in a designated spatial hierarchy (e.g., urban area, city, neighborhood). It is also possible to exploit ancillary data, for example, using property values as a guide in a spatial sampling scheme to measure educational attainment and income. Spatial models such as autocorrelation statistics, regression and interpolation (see below) can also dictate sample design.^{[citation needed]}

Spatial sampling involves determining a limited number of locations in geographic space for faithfully measuring phenomena that are subject to dependency and heterogeneity. Dependency suggests that since one location can predict the value of another location, we do not need observations in both places. But heterogeneity suggests that this relation can change across space, and therefore we cannot trust an observed degree of dependency beyond a region that may be small. Basic spatial sampling schemes include random, clustered and systematic. These basic schemes can be applied at multiple levels in a designated spatial hierarchy (e.g., urban area, city, neighborhood). It is also possible to exploit ancillary data, for example, using property values as a guide in a spatial sampling scheme to measure educational attainment and income. Spatial models such as autocorrelation statistics, regression and interpolation (see below) can also dictate sample design.

= = = 抽样 = = = 空间抽样涉及确定地理空间中有限的几个位置，以便忠实地测量受依赖性和异质性影响的现象。依赖性表明，由于一个位置可以预测另一个位置的价值，我们不需要在两个地方都进行观测。但是，异质性表明，这种关系可以跨空间变化，因此，我们不能相信一个可观察到的依赖程度超过一个区域可能很小。基本的空间抽样方案包括随机抽样、聚类抽样和系统抽样。这些基本方案可以在一个指定的空间层次结构(例如，城市地区、城市、邻里)的多个层次上应用。利用辅助数据也是可能的，例如，在空间抽样方案中使用财产价值作为指导来衡量学历和收入。空间模型，如自相关统计，回归和插值(见下文)也可以指示样本设计。

### Common errors in spatial analysis

The fundamental issues in spatial analysis lead to numerous problems in analysis including bias, distortion and outright errors in the conclusions reached. These issues are often interlinked but various attempts have been made to separate out particular issues from each other.^{[7]}

The fundamental issues in spatial analysis lead to numerous problems in analysis including bias, distortion and outright errors in the conclusions reached. These issues are often interlinked but various attempts have been made to separate out particular issues from each other.

= = 空间分析中的常见错误 = = 空间分析中的基本问题导致分析中的许多问题，包括所得结论的偏差、扭曲和彻底错误。这些问题往往是相互关联的，但已作出各种努力，将特定问题彼此分开。

#### Length

In discussing the coastline of Britain, Benoit Mandelbrot showed that certain spatial concepts are inherently nonsensical despite presumption of their validity. Lengths in ecology depend directly on the scale at which they are measured and experienced. So while surveyors commonly measure the length of a river, this length only has meaning in the context of the relevance of the measuring technique to the question under study.模板:CN

- Britain-fractal-coastline-200km.png
Britain measured using a long yardstick

- Britain-fractal-coastline-100km.png
Britain measured using a medium yardstick

- Britain-fractal-coastline-50km.png
Britain measured using a short yardstick

In discussing the coastline of Britain, Benoit Mandelbrot showed that certain spatial concepts are inherently nonsensical despite presumption of their validity. Lengths in ecology depend directly on the scale at which they are measured and experienced. So while surveyors commonly measure the length of a river, this length only has meaning in the context of the relevance of the measuring technique to the question under study.

Image:britain-fractal-coastline-200km.png|Britain measured using a long yardstick Image:britain-fractal-coastline-100km.png|Britain measured using a medium yardstick Image:britain-fractal-coastline-50km.png|Britain measured using a short yardstick

在讨论英国的海岸线时，本华·曼德博表明，某些空间概念本质上是荒谬的，尽管它们的有效性得到了推定。生态学的长度直接取决于它们被测量和经验的规模。因此，虽然测量员通常测量河流的长度，但这个长度只有在测量技术与所研究问题的相关性的背景下才有意义。图片: 不列颠-分形-海岸线-200公里 png | 英国用长尺测量图片: 不列颠-分形-海岸线-100公里 png | 英国用中尺测量图片: 不列颠-分形-海岸线-50公里 png | 英国用短尺测量

#### Locational fallacy

The locational fallacy refers to error due to the particular spatial characterization chosen for the elements of study, in particular choice of placement for the spatial presence of the element.模板:Cn

The locational fallacy refers to error due to the particular spatial characterization chosen for the elements of study, in particular choice of placement for the spatial presence of the element.

位置谬误指的是由于研究元素选择了特定的空间角色塑造，特别是元素空间存在的位置选择而产生的错误。

Spatial characterizations may be simplistic or even wrong. Studies of humans often reduce the spatial existence of humans to a single point, for instance their home address. This can easily lead to poor analysis, for example, when considering disease transmission which can happen at work or at school and therefore far from the home.模板:Cn

Spatial characterizations may be simplistic or even wrong. Studies of humans often reduce the spatial existence of humans to a single point, for instance their home address. This can easily lead to poor analysis, for example, when considering disease transmission which can happen at work or at school and therefore far from the home.

空间描述可能过于简单，甚至是错误的。对人类的研究常常将人类的空间存在缩小到一个点，例如他们的家庭住址。这很容易导致分析不足，例如，当考虑到疾病传播可能发生在工作或学校，因此远离家庭。

The spatial characterization may implicitly limit the subject of study. For example, the spatial analysis of crime data has recently become popular but these studies can only describe the particular kinds of crime which can be described spatially. This leads to many maps of assault but not to any maps of embezzlement with political consequences in the conceptualization of crime and the design of policies to address the issue.^{[8]}

The spatial characterization may implicitly limit the subject of study. For example, the spatial analysis of crime data has recently become popular but these studies can only describe the particular kinds of crime which can be described spatially. This leads to many maps of assault but not to any maps of embezzlement with political consequences in the conceptualization of crime and the design of policies to address the issue.

空间角色塑造可能隐含地限制了研究对象。例如，犯罪数据的空间分析最近变得流行起来，但这些研究只能描述可以空间描述的特定类型的犯罪。这导致出现了许多袭击地图，但没有出现任何在犯罪概念化和设计解决这一问题的政策方面具有政治后果的贪污地图。

#### Atomic fallacy

This describes errors due to treating elements as separate 'atoms' outside of their spatial context. The fallacy is about transferring individual conclusions to spatial units.^{[9]}

This describes errors due to treating elements as separate 'atoms' outside of their spatial context. The fallacy is about transferring individual conclusions to spatial units.

= = = = = 原子谬误这里描述的错误是把元素看作是空间上下文之外的独立的原子。谬误在于将个体的结论转移到空间单元。

#### Ecological fallacy

The ecological fallacy describes errors due to performing analyses on aggregate data when trying to reach conclusions on the individual units.^{[10]} Errors occur in part from spatial aggregation. For example, a pixel represents the average surface temperatures within an area. Ecological fallacy would be to assume that all points within the area have the same temperature.

The ecological fallacy describes errors due to performing analyses on aggregate data when trying to reach conclusions on the individual units. Errors occur in part from spatial aggregation. For example, a pixel represents the average surface temperatures within an area. Ecological fallacy would be to assume that all points within the area have the same temperature.

= = = = 区群谬误 = = = = = 美国区群谬误统计局描述了由于在试图得出单个单位的结论时对聚合数据进行分析而产生的错误。误差部分来自空间聚集。例如，一个像素代表一个区域内的平均表面温度。区群谬误是假设该区域内的所有点都有相同的温度。

### Solutions to the fundamental issues

### Solutions to the fundamental issues

# = 基本问题的解决方案 =

#### Geographic space

A mathematical space exists whenever we have a set of observations and quantitative measures of their attributes. For example, we can represent individuals' incomes or years of education within a coordinate system where the location of each individual can be specified with respect to both dimensions. The distance between individuals within this space is a quantitative measure of their differences with respect to income and education. However, in spatial analysis, we are concerned with specific types of mathematical spaces, namely, geographic space. In geographic space, the observations correspond to locations in a spatial measurement framework that capture their proximity in the real world. The locations in a spatial measurement framework often represent locations on the surface of the Earth, but this is not strictly necessary. A spatial measurement framework can also capture proximity with respect to, say, interstellar space or within a biological entity such as a liver. The fundamental tenet is Tobler's First Law of Geography: if the interrelation between entities increases with proximity in the real world, then representation in geographic space and assessment using spatial analysis techniques are appropriate.

thumb|200px|Manhattan distance versus Euclidean distance: The red, blue, and yellow lines have the same length (12) in both Euclidean and taxicab geometry. In Euclidean geometry, the green line has length 6× ≈ 8.48, and is the unique shortest path. In taxicab geometry, the green line's length is still 12, making it no shorter than any other path shown.A mathematical space exists whenever we have a set of observations and quantitative measures of their attributes. For example, we can represent individuals' incomes or years of education within a coordinate system where the location of each individual can be specified with respect to both dimensions. The distance between individuals within this space is a quantitative measure of their differences with respect to income and education. However, in spatial analysis, we are concerned with specific types of mathematical spaces, namely, geographic space. In geographic space, the observations correspond to locations in a spatial measurement framework that capture their proximity in the real world. The locations in a spatial measurement framework often represent locations on the surface of the Earth, but this is not strictly necessary. A spatial measurement framework can also capture proximity with respect to, say, interstellar space or within a biological entity such as a liver. The fundamental tenet is Tobler's First Law of Geography: if the interrelation between entities increases with proximity in the real world, then representation in geographic space and assessment using spatial analysis techniques are appropriate.

= = = = 地理空间 = = = 拇指 | 200px | 曼哈顿距离与欧几里得度量: 红色、蓝色和黄色的线在欧几里德几何学和曼哈顿距离几何学中都有相同的长度。在欧几里得几何，绿线的长度是6 × ≈8.48，是唯一的最短路径。在21曼哈顿距离，绿线的长度仍然是12，并不比其他路径显示的短。每当我们有一组观测数据和对它们属性的定量度量时，数学空间就存在了。例如，我们可以用一个坐标系来表示个人的收入或者受教育的年数，在这个范围内，每个人的位置都可以在两个方面都被指定。在这个空间内个人之间的距离是衡量他们在收入和教育方面差异的一个量化尺度。然而，在空间分析中，我们关注的是特定类型的数学空间，即地理空间。在地理空间中，观测对应于空间测量框架中的位置，这些位置在现实世界中捕捉到了它们的接近程度。空间测量框架中的位置通常代表地球表面的位置，但这并非绝对必要。一个空间测量框架也可以捕获星际空间或者生物实体如肝脏的邻近性。基本原则是托布勒的第一地理定律: 如果实体之间的相互关系在现实世界中随着接近程度的增加而增加，那么在地理空间中进行表示和使用空间分析技术进行评估是适当的。

The Euclidean distance between locations often represents their proximity, although this is only one possibility. There are an infinite number of distances in addition to Euclidean that can support quantitative analysis. For example, "Manhattan" (or "Taxicab") distances where movement is restricted to paths parallel to the axes can be more meaningful than Euclidean distances in urban settings. In addition to distances, other geographic relationships such as connectivity** (e.g., the existence or degree of shared borders) and direction** can also influence the relationships among entities. It is also possible to compute minimal cost paths across a cost surface; for example, this can represent proximity among locations when travel must occur across rugged terrain.

The Euclidean distance between locations often represents their proximity, although this is only one possibility. There are an infinite number of distances in addition to Euclidean that can support quantitative analysis. For example, "Manhattan" (or "Taxicab") distances where movement is restricted to paths parallel to the axes can be more meaningful than Euclidean distances in urban settings. In addition to distances, other geographic relationships such as connectivity (e.g., the existence or degree of shared borders) and direction can also influence the relationships among entities. It is also possible to compute minimal cost paths across a cost surface; for example, this can represent proximity among locations when travel must occur across rugged terrain.

位置之间的欧几里得度量通常代表它们的接近程度，尽管这只是一种可能性。除了欧几里德几何之外，还有无数的距离可以支持定量分析。例如，“曼哈顿”(或“出租车”)的距离移动是限制路径平行轴可以更有意义比欧几里德距离在城市环境。除了距离之外，其他地理关系，如连通性(例如，共享边界的存在或程度)和方向也可以影响实体之间的关系。还可以计算成本曲面上的最小成本路径; 例如，当必须在崎岖的地形上旅行时，这可以表示位置之间的接近程度。

## Types

Spatial data comes in many varieties and it is not easy to arrive at a system of classification that is simultaneously exclusive, exhaustive, imaginative, and satisfying. -- G. Upton & B. Fingelton

^{[11]}

Spatial data comes in many varieties and it is not easy to arrive at a system of classification that is simultaneously exclusive, exhaustive, imaginative, and satisfying. -- G. Upton & B. FingeltonGraham J. Upton & Bernard Fingelton: Spatial Data Analysis by Example Volume 1: Point Pattern and Quantitative Data John Wiley & Sons, New York. 1985.

= = = = 空间数据有许多种类，要同时达到排他性、详尽性、想象性和令人满意的分类系统是不容易的。约翰威立: 空间数据分析，例子第一卷: 点模式和定量数据，纽约。1985.

### Spatial data analysis

Urban and Regional Studies deal with large tables of spatial data obtained from censuses and surveys. It is necessary to simplify the huge amount of detailed information in order to extract the main trends. Multivariable analysis (or Factor analysis, FA) allows a change of variables, transforming the many variables of the census, usually correlated between themselves, into fewer independent "Factors" or "Principal Components" which are, actually, the eigenvectors of the data correlation matrix weighted by the inverse of their eigenvalues. This change of variables has two main advantages:

- Since information is concentrated on the first new factors, it is possible to keep only a few of them while losing only a small amount of information; mapping them produces fewer and more significant maps
- The factors, actually the eigenvectors, are orthogonal by construction, i.e. not correlated. In most cases, the dominant factor (with the largest eigenvalue) is the Social Component, separating rich and poor in the city. Since factors are not-correlated, other smaller processes than social status, which would have remained hidden otherwise, appear on the second, third, ... factors.

Urban and Regional Studies deal with large tables of spatial data obtained from censuses and surveys. It is necessary to simplify the huge amount of detailed information in order to extract the main trends. Multivariable analysis (or Factor analysis, FA) allows a change of variables, transforming the many variables of the census, usually correlated between themselves, into fewer independent "Factors" or "Principal Components" which are, actually, the eigenvectors of the data correlation matrix weighted by the inverse of their eigenvalues. This change of variables has two main advantages:

- Since information is concentrated on the first new factors, it is possible to keep only a few of them while losing only a small amount of information; mapping them produces fewer and more significant maps
- The factors, actually the eigenvectors, are orthogonal by construction, i.e. not correlated. In most cases, the dominant factor (with the largest eigenvalue) is the Social Component, separating rich and poor in the city. Since factors are not-correlated, other smaller processes than social status, which would have remained hidden otherwise, appear on the second, third, ... factors.

= = = 空间数据分析 = = = 城市和区域研究处理从人口普查和调查中获得的大量空间数据表。为了提取主要趋势，有必要对海量的详细信息进行简化。多变量分析(或因素分析)允许变量的变化，将普查中许多变量(通常彼此相关)转化为较少的独立”因素”或”主成分”，这些因素实际上是数据相关矩阵的特征向量，其特征值的倒数加权。这种变量的变化有两个主要的优点: # 由于信息集中在第一个新因子上，所以只能保留其中的少数几个因子，同时只丢失少量的信息; 映射它们产生的地图越来越少，越来越有意义 # 这些因子，实际上是特征向量，是正交的结构，即。不相关的。在大多数情况下，主导因素(具有最大的特征值)是社会成分，在城市中分离富人和穷人。因为这些因素是不相关的，其他比社会地位更小的过程，如果不是这样就会被隐藏起来，会出现在第二、第三、 ... ... 因素中。

Factor analysis depends on measuring distances between observations : the choice of a significant metric is crucial. The Euclidean metric (Principal Component Analysis), the Chi-Square distance (Correspondence Analysis) or the Generalized Mahalanobis distance (Discriminant Analysis) are among the more widely used.^{[12]} More complicated models, using communalities or rotations have been proposed.^{[13]}

Factor analysis depends on measuring distances between observations : the choice of a significant metric is crucial. The Euclidean metric (Principal Component Analysis), the Chi-Square distance (Correspondence Analysis) or the Generalized Mahalanobis distance (Discriminant Analysis) are among the more widely used.Harman H H (1960) Modern Factor Analysis, University of Chicago Press More complicated models, using communalities or rotations have been proposed.Rummel R J (1970) Applied Factor Analysis. Evanston, ILL: Northwestern University Press.

因子分析依赖于测量观察值之间的距离: 重要度量的选择是关键的。欧氏度量(欧氏主成分分析)、 Chi-Square 距离(对应分析)或广义马氏距离(判别分析)是其中应用较为广泛的。哈曼 h (1960)现代因子分析，芝加哥大学出版社更复杂的模型，使用公有性或轮换已被提出。Rummel r j (1970)应用因子分析。埃文斯顿，ILL: 西北大学。

Using multivariate methods in spatial analysis began really in the 1950s (although some examples go back to the beginning of the century) and culminated in the 1970s, with the increasing power and accessibility of computers. Already in 1948, in a seminal publication, two sociologists, Wendell Bell and Eshref Shevky,^{[14]} had shown that most city populations in the US and in the world could be represented with three independent factors : 1- the « socio-economic status » opposing rich and poor districts and distributed in sectors running along highways from the city center, 2- the « life cycle », i.e. the age structure of households, distributed in concentric circles, and 3- « race and ethnicity », identifying patches of migrants located within the city. In 1961, in a groundbreaking study, British geographers used FA to classify British towns.^{[15]} Brian J Berry, at the University of Chicago, and his students made a wide use of the method,^{[16]} applying it to most important cities in the world and exhibiting common social structures.^{[17]}
The use of Factor Analysis in Geography, made so easy by modern computers, has been very wide but not always very wise.^{[18]}

Using multivariate methods in spatial analysis began really in the 1950s (although some examples go back to the beginning of the century) and culminated in the 1970s, with the increasing power and accessibility of computers. Already in 1948, in a seminal publication, two sociologists, Wendell Bell and Eshref Shevky,Bell W & E Shevky (1955) Social Area Analysis, Stanford University Press had shown that most city populations in the US and in the world could be represented with three independent factors : 1- the « socio-economic status » opposing rich and poor districts and distributed in sectors running along highways from the city center, 2- the « life cycle », i.e. the age structure of households, distributed in concentric circles, and 3- « race and ethnicity », identifying patches of migrants located within the city. In 1961, in a groundbreaking study, British geographers used FA to classify British towns.Moser C A & W Scott (1961) British Towns ; A Statistical Study of their Social and Economic Differences, Oliver & Boyd, London. Brian J Berry, at the University of Chicago, and his students made a wide use of the method,Berry B J & F Horton (1971) Geographic Perspectives on Urban Systems, John Wiley, N-Y. applying it to most important cities in the world and exhibiting common social structures.Berry B J & K B Smith eds (1972) City Classification Handbook : Methods and Applications, John Wiley, N-Y. The use of Factor Analysis in Geography, made so easy by modern computers, has been very wide but not always very wise.Ciceri M-F (1974) Méthodes d’analyse multivariée dans la géographie anglo-saxonne, Université de Paris-1 ; free download on http://www-ohp.univ-paris1.fr

在空间分析中使用多元方法实际上始于20世纪50年代(尽管有些例子可以追溯到本世纪初) ，并在20世纪70年代达到顶峰，随着计算机能力和可及性的增加。早在1948年，在一个开创性的出版物中，两位社会学家，Wendell Bell 和 Eshref Shevky，Bell w & e Shevky (1955)社会区域分析，Stanford University Press 已经表明，美国和世界上大多数城市人口可以用三个独立的因素来代表: 1——反对富裕和贫穷地区的”社会经济地位”，分布在从市中心沿高速公路运行的部门; 2——”生命周期”，即”生命周期”。以同心圆形分布的家庭年龄结构，以及3个“种族和民族”，识别城市内部的移民群体。1961年，在一项开创性的研究中，英国地理学家利用 FA 对英国城镇进行了分类。Moser c a & w Scott (1961) British Towns; a Statistical Study of their Social and Economic Differences，Oliver & Boyd，London.芝加哥大学的 Brian j Berry 和他的学生们广泛使用了这种方法，Berry b j & f Horton (1971) Geographic Perspectives on Urban Systems，John Wiley，N-Y。将其应用于世界上最重要的城市，并展示出共同的社会结构。贝里 b & k b 史密斯编(1972)城市分类手册: 方法和应用，约翰威利，N-Y。现代计算机使得因素分析在地理学中的应用变得非常简单，虽然应用范围很广，但并不总是很明智。Ciceri M-F (1974) m’thodes d’analyse multivariée dans la géographie anglo-saxonne，Université de Paris-1; 免费下载 http://www-ohp.univ-paris1.fr

Since the vectors extracted are determined by the data matrix, it is not possible to compare factors obtained from different censuses. A solution consists in fusing together several census matrices in a unique table which, then, may be analyzed. This, however, assumes that the definition of the variables has not changed over time and produces very large tables, difficult to manage. A better solution, proposed by psychometricians,^{[19]} groups the data in a « cubic matrix », with three entries (for instance, locations, variables, time periods). A Three-Way Factor Analysis produces then three groups of factors related by a small cubic « core matrix ».^{[20]} This method, which exhibits data evolution over time, has not been widely used in geography.^{[21]} In Los Angeles,^{[22]} however, it has exhibited the role, traditionally ignored, of Downtown as an organizing center for the whole city during several decades.

Since the vectors extracted are determined by the data matrix, it is not possible to compare factors obtained from different censuses. A solution consists in fusing together several census matrices in a unique table which, then, may be analyzed. This, however, assumes that the definition of the variables has not changed over time and produces very large tables, difficult to manage. A better solution, proposed by psychometricians,Tucker L R (1964) « The extension of Factor Analysis to three-dimensional matrices », in Frederiksen N & H Gulliksen eds, Contributions to Mathematical Psychology, Holt, Rinehart and Winston, NY. groups the data in a « cubic matrix », with three entries (for instance, locations, variables, time periods). A Three-Way Factor Analysis produces then three groups of factors related by a small cubic « core matrix ».R. Coppi & S. Bolasco, eds. (1989), Multiway data analysis, Elsevier, Amsterdam. This method, which exhibits data evolution over time, has not been widely used in geography. In Los Angeles,Marchand B (1986) The Emergence of Los Angeles, 1940-1970, Pion Ltd, London however, it has exhibited the role, traditionally ignored, of Downtown as an organizing center for the whole city during several decades.

由于提取的向量是由数据矩阵确定的，因此不可能比较从不同普查中获得的因素。一个解决方案是将几个普查矩阵融合在一个唯一的表中，然后可以对其进行分析。然而，这是假设变量的定义没有随着时间的推移而改变，并且生成非常大的表，这很难管理。心理测量学家 Tucker l r (1964)在 Frederiksen n & h Gulliksen eds，Contributions to Mathematical Psychology，Holt，Rinehart and Winston，NY 中提出了一个更好的解决方案，“因子分析在三维矩阵中的扩展”。用三个条目(例如，位置、变量和时间周期)将数据分组为“立方矩阵”。通过三因素分析，得到了三组与小立方体“核心矩阵”相关的因素。Coppi & S. Bolasco, eds.(1989) ，Multiway data analysis，Elsevier，Amsterdam.这种方法显示了数据随时间的演化过程，在地理学中尚未得到广泛应用。在洛杉矶，Marchand b (1986)洛杉矶的兴起，1940-1970，Pion Ltd，伦敦然而，它展示了传统上被忽视的作用，市中心作为整个城市的组织中心，在几十年里。

### Spatial autocorrelation

Spatial autocorrelation statistics measure and analyze the degree of dependency among observations in a geographic space. Classic spatial autocorrelation statistics include Moran's [math]\displaystyle{ I }[/math], Geary's [math]\displaystyle{ C }[/math], Getis's [math]\displaystyle{ G }[/math] and the standard deviational ellipse. These statistics require measuring a spatial weights matrix that reflects the intensity of the geographic relationship between observations in a neighborhood, e.g., the distances between neighbors, the lengths of shared border, or whether they fall into a specified directional class such as "west". Classic spatial autocorrelation statistics compare the spatial weights to the covariance relationship at pairs of locations. Spatial autocorrelation that is more positive than expected from random indicate the clustering of similar values across geographic space, while significant negative spatial autocorrelation indicates that neighboring values are more dissimilar than expected by chance, suggesting a spatial pattern similar to a chess board.

Spatial autocorrelation statistics measure and analyze the degree of dependency among observations in a geographic space. Classic spatial autocorrelation statistics include Moran's I, Geary's C, Getis's G and the standard deviational ellipse. These statistics require measuring a spatial weights matrix that reflects the intensity of the geographic relationship between observations in a neighborhood, e.g., the distances between neighbors, the lengths of shared border, or whether they fall into a specified directional class such as "west". Classic spatial autocorrelation statistics compare the spatial weights to the covariance relationship at pairs of locations. Spatial autocorrelation that is more positive than expected from random indicate the clustering of similar values across geographic space, while significant negative spatial autocorrelation indicates that neighboring values are more dissimilar than expected by chance, suggesting a spatial pattern similar to a chess board.

= = = 空间自相关 = = = 空间自相关统计测量和分析在一个地理空间观测的依赖程度。经典的空间自相关统计量包括 Moran 的 i，Geary 的 c，Getis 的 g 和标准偏离椭圆。这些统计数据需要测量一个空间权重矩阵，该矩阵反映了邻近观测值之间的地理关系的强度，例如邻居之间的距离、共享边界的长度，或者它们是否属于指定的方向类别，例如“西”。经典的空间自相关统计比较空间权重协方差关系在成对的位置。空间自相关比随机的预期更正表明了相似值在整个地理空间的聚类，而显著的负空间自相关表明相邻值比随机的预期更不相似，表明空间模式类似于国际象棋棋盘。

Spatial autocorrelation statistics such as Moran's [math]\displaystyle{ I }[/math] and Geary's [math]\displaystyle{ C }[/math] are global in the sense that they estimate the overall degree of spatial autocorrelation for a dataset. The possibility of spatial heterogeneity suggests that the estimated degree of autocorrelation may vary significantly across geographic space. **Local spatial autocorrelation statistics** provide estimates disaggregated to the level of the spatial analysis units, allowing assessment of the dependency relationships across space. [math]\displaystyle{ G }[/math] statistics compare neighborhoods to a global average and identify local regions of strong autocorrelation. Local versions of the [math]\displaystyle{ I }[/math] and [math]\displaystyle{ C }[/math] statistics are also available.

Spatial autocorrelation statistics such as Moran's I and Geary's C are global in the sense that they estimate the overall degree of spatial autocorrelation for a dataset. The possibility of spatial heterogeneity suggests that the estimated degree of autocorrelation may vary significantly across geographic space. Local spatial autocorrelation statistics provide estimates disaggregated to the level of the spatial analysis units, allowing assessment of the dependency relationships across space. G statistics compare neighborhoods to a global average and identify local regions of strong autocorrelation. Local versions of the I and C statistics are also available.

空间自相关统计学如 Moran 的 i 和 Geary 的 c 是全局的，因为它们估计了数据集的空间自相关的整体程度。空间异质性的可能性表明，估计的自相关程度可能在不同的地理空间有显著差异。当地空间自相关统计数据提供按空间分析单位水平分列的估计数，从而可以评估各空间的依赖关系。G 统计数据将社区与全球平均值进行比较，并确定具有强自相关性的局部地区。I 和 c 统计数据的本地版本也可用。

### Spatial heterogeneity

### Spatial interpolation

Spatial interpolation methods estimate the variables at unobserved locations in geographic space based on the values at observed locations. Basic methods include inverse distance weighting: this attenuates the variable with decreasing proximity from the observed location. Kriging is a more sophisticated method that interpolates across space according to a spatial lag relationship that has both systematic and random components. This can accommodate a wide range of spatial relationships for the hidden values between observed locations. Kriging provides optimal estimates given the hypothesized lag relationship, and error estimates can be mapped to determine if spatial patterns exist.

Spatial interpolation methods estimate the variables at unobserved locations in geographic space based on the values at observed locations. Basic methods include inverse distance weighting: this attenuates the variable with decreasing proximity from the observed location. Kriging is a more sophisticated method that interpolates across space according to a spatial lag relationship that has both systematic and random components. This can accommodate a wide range of spatial relationships for the hidden values between observed locations. Kriging provides optimal estimates given the hypothesized lag relationship, and error estimates can be mapped to determine if spatial patterns exist.

= = = 空间插值 = = = 空间插值方法根据观测点的值估计地理空间未观测点的变量。基本的方法包括反向距离加权: 这衰减的变量与降低接近从观测位置。克里格法是一种更为复杂的方法，它根据一种既有系统成分又有随机成分的空间滞后关系进行空间插值。这可以容纳观测位置之间隐藏值的广泛空间关系。克立格法给出了假设的滞后关系的最优估计，并且可以通过映射误差估计来确定是否存在空间模式。

### Spatial regression

Spatial regression methods capture spatial dependency in regression analysis, avoiding statistical problems such as unstable parameters and unreliable significance tests, as well as providing information on spatial relationships among the variables involved. Depending on the specific technique, spatial dependency can enter the regression model as relationships between the independent variables and the dependent, between the dependent variables and a spatial lag of itself, or in the error terms. **Geographically weighted regression** (GWR) is a local version of spatial regression that generates parameters disaggregated by the spatial units of analysis.^{[23]} This allows assessment of the spatial heterogeneity in the estimated relationships between the independent and dependent variables. The use of Bayesian hierarchical modeling^{[24]} in conjunction with Markov chain Monte Carlo (MCMC) methods have recently shown to be effective in modeling complex relationships using Poisson-Gamma-CAR, Poisson-lognormal-SAR, or Overdispersed logit models. Statistical packages for implementing such Bayesian models using MCMC include WinBugs, CrimeStat and many packages available via R programming language.^{[25]}

Spatial regression methods capture spatial dependency in regression analysis, avoiding statistical problems such as unstable parameters and unreliable significance tests, as well as providing information on spatial relationships among the variables involved. Depending on the specific technique, spatial dependency can enter the regression model as relationships between the independent variables and the dependent, between the dependent variables and a spatial lag of itself, or in the error terms. Geographically weighted regression (GWR) is a local version of spatial regression that generates parameters disaggregated by the spatial units of analysis. This allows assessment of the spatial heterogeneity in the estimated relationships between the independent and dependent variables. The use of Bayesian hierarchical modeling in conjunction with Markov chain Monte Carlo (MCMC) methods have recently shown to be effective in modeling complex relationships using Poisson-Gamma-CAR, Poisson-lognormal-SAR, or Overdispersed logit models. Statistical packages for implementing such Bayesian models using MCMC include WinBugs, CrimeStat and many packages available via R programming language.

空间回归方法捕捉回归分析的空间依赖性，避免统计问题，如不稳定的参数和不可靠的显著性检验，以及提供有关变量之间的空间关系的信息。根据具体的技术，空间依赖性可以作为自变量与依赖变量之间、依赖变量与自身的空间滞后之间或误差项之间的关系进入回归模型。地理加权回归(GWR)是一种局部形式的空间回归，它产生按空间单位分列的参数。这允许评估空间异质性之间的独立和因变量的估计关系。使用贝叶斯层次建模结合马尔科夫蒙特卡洛方法(MCMC)的方法，最近被证明在使用 Poisson-Gamma-CAR，Poisson-lognormal-SAR，或过度分散 logit 模型建模复杂关系时是有效的。使用 MCMC 实现这种贝叶斯模型的统计软件包包括 WinBugs、 CrimeStat 和许多通过 r 编程语言可用的软件包。

Spatial stochastic processes, such as Gaussian processes are also increasingly being deployed in spatial regression analysis. Model-based versions of GWR, known as spatially varying coefficient models have been applied to conduct Bayesian inference.^{[24]} Spatial stochastic process can become computationally effective and scalable Gaussian process models, such as Gaussian Predictive Processes^{[26]} and Nearest Neighbor Gaussian Processes (NNGP).^{[27]}

Spatial stochastic processes, such as Gaussian processes are also increasingly being deployed in spatial regression analysis. Model-based versions of GWR, known as spatially varying coefficient models have been applied to conduct Bayesian inference. Spatial stochastic process can become computationally effective and scalable Gaussian process models, such as Gaussian Predictive Processes and Nearest Neighbor Gaussian Processes (NNGP).

空间随机过程，如高斯过程也越来越多地被部署在空间回归分析。基于模型的 GWR 版本，被称为空间变化系数模型，已经被应用于进行贝叶斯推断。空间随机过程可以成为计算有效和可扩展的高斯过程模型，如高斯预测过程和最近邻高斯过程。

### Spatial interaction

Spatial interaction or "gravity models" estimate the flow of people, material or information between locations in geographic space. Factors can include origin propulsive variables such as the number of commuters in residential areas, destination attractiveness variables such as the amount of office space in employment areas, and proximity relationships between the locations measured in terms such as driving distance or travel time. In addition, the topological, or connective, relationships between areas must be identified, particularly considering the often conflicting relationship between distance and topology; for example, two spatially close neighborhoods may not display any significant interaction if they are separated by a highway. After specifying the functional forms of these relationships, the analyst can estimate model parameters using observed flow data and standard estimation techniques such as ordinary least squares or maximum likelihood. Competing destinations versions of spatial interaction models include the proximity among the destinations (or origins) in addition to the origin-destination proximity; this captures the effects of destination (origin) clustering on flows. Computational methods such as artificial neural networks can also estimate spatial interaction relationships among locations and can handle noisy and qualitative data.^{[citation needed]}

Spatial interaction or "gravity models" estimate the flow of people, material or information between locations in geographic space. Factors can include origin propulsive variables such as the number of commuters in residential areas, destination attractiveness variables such as the amount of office space in employment areas, and proximity relationships between the locations measured in terms such as driving distance or travel time. In addition, the topological, or connective, relationships between areas must be identified, particularly considering the often conflicting relationship between distance and topology; for example, two spatially close neighborhoods may not display any significant interaction if they are separated by a highway. After specifying the functional forms of these relationships, the analyst can estimate model parameters using observed flow data and standard estimation techniques such as ordinary least squares or maximum likelihood. Competing destinations versions of spatial interaction models include the proximity among the destinations (or origins) in addition to the origin-destination proximity; this captures the effects of destination (origin) clustering on flows. Computational methods such as artificial neural networks can also estimate spatial interaction relationships among locations and can handle noisy and qualitative data.

= = 空间相互作用 = = 空间相互作用或”重力模型”估计人、物质或信息在地理空间位置之间的流动。因素可以包括原点推进变量，如居住区的通勤者数量，目的地吸引力变量，如就业区的办公空间数量，以及以驾驶距离或出行时间衡量的地点之间的邻近关系。此外，区域之间的拓扑关系，或者说连接关系必须被识别，特别是考虑到距离和拓扑之间的冲突关系; 例如，两个空间上相近的邻居如果被高速公路分开，可能不会显示任何显著的相互作用。在指定了这些关系的功能形式之后，分析人员可以使用观测流数据和标准估计技术，如一般最小平方法或最大似然估计模型参数。空间互动模型的竞争目的地版本包括目的地(或起源地)之间的距离以及起源地和目的地之间的距离; 这捕获了目的地(起源地)集群对流动的影响。人工神经网络等计算方法还可以估计位置之间的空间相互作用关系，并能处理噪声和定性数据。

### Simulation and modeling

Spatial interaction models are aggregate and top-down: they specify an overall governing relationship for flow between locations. This characteristic is also shared by urban models such as those based on mathematical programming, flows among economic sectors, or bid-rent theory. An alternative modeling perspective is to represent the system at the highest possible level of disaggregation and study the bottom-up emergence of complex patterns and relationships from behavior and interactions at the individual level.^{[citation needed]}

Spatial interaction models are aggregate and top-down: they specify an overall governing relationship for flow between locations. This characteristic is also shared by urban models such as those based on mathematical programming, flows among economic sectors, or bid-rent theory. An alternative modeling perspective is to represent the system at the highest possible level of disaggregation and study the bottom-up emergence of complex patterns and relationships from behavior and interactions at the individual level.

= = = 仿真和建模 = = = 空间交互模型是集合的和自上而下的: 它们为位置之间的流动指定了一个总体的控制关系。这一特点也为城市模型所共享，如那些基于数学规划、经济部门之间的流动或出租理论的城市模型。另一种建模视角是以尽可能高的分解级别来表示系统，并研究从个体级别的行为和交互中自下而上出现的复杂模式和关系。

Complex adaptive systems theory as applied to spatial analysis suggests that simple interactions among proximal entities can lead to intricate, persistent and functional spatial entities at aggregate levels. Two fundamentally spatial simulation methods are cellular automata and agent-based modeling. Cellular automata modeling imposes a fixed spatial framework such as grid cells and specifies rules that dictate the state of a cell based on the states of its neighboring cells. As time progresses, spatial patterns emerge as cells change states based on their neighbors; this alters the conditions for future time periods. For example, cells can represent locations in an urban area and their states can be different types of land use. Patterns that can emerge from the simple interactions of local land uses include office districts and urban sprawl. Agent-based modeling uses software entities (agents) that have purposeful behavior (goals) and can react, interact and modify their environment while seeking their objectives. Unlike the cells in cellular automata, simulysts can allow agents to be mobile with respect to space. For example, one could model traffic flow and dynamics using agents representing individual vehicles that try to minimize travel time between specified origins and destinations. While pursuing minimal travel times, the agents must avoid collisions with other vehicles also seeking to minimize their travel times. Cellular automata and agent-based modeling are complementary modeling strategies. They can be integrated into a common geographic automata system where some agents are fixed while others are mobile.

Complex adaptive systems theory as applied to spatial analysis suggests that simple interactions among proximal entities can lead to intricate, persistent and functional spatial entities at aggregate levels. Two fundamentally spatial simulation methods are cellular automata and agent-based modeling. Cellular automata modeling imposes a fixed spatial framework such as grid cells and specifies rules that dictate the state of a cell based on the states of its neighboring cells. As time progresses, spatial patterns emerge as cells change states based on their neighbors; this alters the conditions for future time periods. For example, cells can represent locations in an urban area and their states can be different types of land use. Patterns that can emerge from the simple interactions of local land uses include office districts and urban sprawl. Agent-based modeling uses software entities (agents) that have purposeful behavior (goals) and can react, interact and modify their environment while seeking their objectives. Unlike the cells in cellular automata, simulysts can allow agents to be mobile with respect to space. For example, one could model traffic flow and dynamics using agents representing individual vehicles that try to minimize travel time between specified origins and destinations. While pursuing minimal travel times, the agents must avoid collisions with other vehicles also seeking to minimize their travel times. Cellular automata and agent-based modeling are complementary modeling strategies. They can be integrated into a common geographic automata system where some agents are fixed while others are mobile.

应用于空间分析的复杂适应系统理论表明，近端实体之间的简单相互作用可以在聚集层次上导致复杂、持久和功能性的空间实体。元胞自动机和基于主体的建模是两种基本的空间模拟方法。细胞自动机建模施加了一个固定的空间框架，如网格细胞，并指定规则，指定状态的细胞基于其邻近细胞的状态。随着时间的推移，空间模式出现，细胞根据它们的邻居改变状态; 这改变了未来时间周期的条件。例如，单元格可以表示城市地区的位置，它们的状态可以是不同类型的土地使用。从当地土地使用的简单互动中可以出现的模式包括办公区和城市扩张。基于 agent 的建模使用软件实体(agent) ，这些实体具有有目的的行为(目标) ，可以在寻找目标的同时对其环境进行反应、交互和修改。与细胞自动机中的细胞不同，模拟器允许代理在空间上可以移动。例如，人们可以使用代表单个车辆的代理程序来模拟交通流和动态，这些代理程序试图最小化指定起点和目的地之间的旅行时间。在追求最小旅行时间的同时，代理商必须避免与其他车辆发生碰撞，同时也要尽量缩短旅行时间。元胞自动机和基于主体的建模是互补的建模策略。它们可以集成到一个常见的地理自动机系统中，其中一些代理是固定的，而另一些代理是移动的。

Calibration plays a pivotal role in both CA and ABM simulation and modelling approaches. Initial approaches to CA proposed robust calibration approaches based on stochastic, Monte Carlo methods.^{[28]}^{[29]} ABM approaches rely on agents' decision rules (in many cases extracted from qualitative research base methods such as questionnaires).^{[30]} Recent Machine Learning Algorithms calibrate using training sets, for instance in order to understand the qualities of the built environment.^{[31]}

Calibration plays a pivotal role in both CA and ABM simulation and modelling approaches. Initial approaches to CA proposed robust calibration approaches based on stochastic, Monte Carlo methods. ABM approaches rely on agents' decision rules (in many cases extracted from qualitative research base methods such as questionnaires). Recent Machine Learning Algorithms calibrate using training sets, for instance in order to understand the qualities of the built environment.

标定在 CA 和 ABM 仿真和建模方法中起着举足轻重的作用。初步提出了基于随机蒙特卡罗方法的稳健校正方法。ABM 方法依赖于代理人的决策规则(在许多情况下，这些决策规则是从质性研究的基础方法如问卷调查中提取出来的)。最近的机器学习算法使用训练集进行校准，例如，为了理解构建环境的质量。

### Multiple-point geostatistics (MPS)

Spatial analysis of a conceptual geological model is the main purpose of any MPS algorithm. The method analyzes the spatial statistics of the geological model, called the training image, and generates realizations of the phenomena that honor those input multiple-point statistics.

Spatial analysis of a conceptual geological model is the main purpose of any MPS algorithm. The method analyzes the spatial statistics of the geological model, called the training image, and generates realizations of the phenomena that honor those input multiple-point statistics.

= = = = 多点地质统计学(MPS) = = = 对概念地质模型进行空间分析是任何 MPS 算法的主要目的。该方法分析地质模型的空间统计量，称为训练图像，并生成符合输入多点统计量的现象的实现。

A recent MPS algorithm used to accomplish this task is the pattern-based method by Honarkhah.^{[32]} In this method, a distance-based approach is employed to analyze the patterns in the training image. This allows the reproduction of the multiple-point statistics, and the complex geometrical features of the training image. Each output of the MPS algorithm is a realization that represents a random field. Together, several realizations may be used to quantify spatial uncertainty.

A recent MPS algorithm used to accomplish this task is the pattern-based method by Honarkhah. In this method, a distance-based approach is employed to analyze the patterns in the training image. This allows the reproduction of the multiple-point statistics, and the complex geometrical features of the training image. Each output of the MPS algorithm is a realization that represents a random field. Together, several realizations may be used to quantify spatial uncertainty.

最近用于完成这项任务的 MPS 算法是 Honarkhah 的基于模式的方法。该方法采用基于距离的方法对训练图像中的模式进行分析。这样就可以重现多点统计信息和训练图像复杂的几何特征。MPS 算法的每个输出都是一个表示随机场的实现。总之，几个实现可以用来量化空间的不确定性。

One of the recent methods is presented by Tahmasebi et al.^{[33]} uses a cross-correlation function to improve the spatial pattern reproduction. They call their MPS simulation method as the CCSIM algorithm. This method is able to quantify the spatial connectivity, variability and uncertainty. Furthermore, the method is not sensitive to any type of data and is able to simulate both categorical and continuous scenarios. CCSIM algorithm is able to be used for any stationary, non-stationary and multivariate systems and it can provide high quality visual appeal model.,^{[34]}^{[35]}

One of the recent methods is presented by Tahmasebi et al. uses a cross-correlation function to improve the spatial pattern reproduction. They call their MPS simulation method as the CCSIM algorithm. This method is able to quantify the spatial connectivity, variability and uncertainty. Furthermore, the method is not sensitive to any type of data and is able to simulate both categorical and continuous scenarios. CCSIM algorithm is able to be used for any stationary, non-stationary and multivariate systems and it can provide high quality visual appeal model.,

最近的一个方法是由 Tahmasebi 等人提出的。使用互相关函数来改善空间模式的复制。他们称他们的 MPS 模拟方法为 CCSIM 算法。该方法能够量化空间连通性、变异性和不确定性。此外，该方法对任何类型的数据都不敏感，能够同时模拟分类场景和连续场景。CCSIM 算法适用于任何平稳、非平稳和多变量系统，能够提供高质量的视觉吸引力模型,

## Geospatial and Hydrospatial analysis

模板:Cleanup merge
**Geospatial and Hydrospatial analysis**, or just **spatial analysis**,^{[36]} is an approach to applying statistical analysis and other analytic techniques to data which has a geographical or spatial aspect. Such analysis would typically employ software capable of rendering maps processing spatial data, and applying analytical methods to terrestrial or geographic datasets, including the use of geographic information systems and geomatics.^{[37]}^{[38]}^{[39]}

Geospatial and Hydrospatial analysis, or just spatial analysis, is an approach to applying statistical analysis and other analytic techniques to data which has a geographical or spatial aspect. Such analysis would typically employ software capable of rendering maps processing spatial data, and applying analytical methods to terrestrial or geographic datasets, including the use of geographic information systems and geomatics.geospatial. Collins English Dictionary - Complete & Unabridged 11th Edition. Retrieved 5tth August 2012 from CollinsDictionary.com website:
http://www.collinsdictionary.com/dictionary/english/geospatialDictionary.com's 21st Century Lexicon Copyright © 2003-2010 Dictionary.com, LLC http://dictionary.reference.com/browse/geospatialThe geospatial web – blending physical and virtual spaces. , Arno Scharl in receiver magazine, Autumn 2008

= = 地理空间和水文空间分析 = = 地理空间和水文空间分析，或仅仅是空间分析，是对具有地理或空间方面的数据应用统计分析和其他分析技术的一种方法。这种分析通常使用能够绘制处理空间数据的地图的软件，并对陆地或地理数据集应用分析方法，包括使用地理信息系统和地理空间信息系统。柯林斯英语词典-完整和完整的第11版。2012年8月5日， collinsdictionary.com 网站: http://www.collinsdictionary.com/dictionary/english/geospatialdictionary.com’s 21st Century Lexicon Copyright 2003-2010 Dictionary.com，LLC http://dictionary.reference.com/browse/geospatialthe 地理空间网络-blending physical and virtual spaces。，《接收者》杂志，2008年秋

### Geographical information system usage

Geographic information systems (GIS) — a large domain that provides a variety of capabilities designed to capture, store, manipulate, analyze, manage, and present all types of geographical data — utilizes geospatial and hydrospatial analysis in a variety of contexts, operations and applications.

Geographic information systems (GIS) — a large domain that provides a variety of capabilities designed to capture, store, manipulate, analyze, manage, and present all types of geographical data — utilizes geospatial and hydrospatial analysis in a variety of contexts, operations and applications.

= = = 地理信息系统的使用 = = = 地理信息系统(GIS)ーー一个提供各种能力的大领域，旨在获取、存储、操作、分析、管理和显示所有类型的地理数据ーー利用地理空间和水文空间分析在各种情况、操作和应用中。

#### Basic applications

Geospatial and Hydrospatial analysis, using GIS, was developed for problems in the environmental and life sciences, in particular ecology, geology and epidemiology. It has extended to almost all industries including defense, intelligence, utilities, Natural Resources (i.e. Oil and Gas, Forestry ... etc.), social sciences, medicine and Public Safety (i.e. emergency management and criminology), disaster risk reduction and management (DRRM), and climate change adaptation (CCA). Spatial statistics typically result primarily from observation rather than experimentation. Hydrospatial is particularly used for the aquatic side and the members related to the water surface, column, bottom, sub-bottom and the coastal zones.

Geospatial and Hydrospatial analysis, using GIS, was developed for problems in the environmental and life sciences, in particular ecology, geology and epidemiology. It has extended to almost all industries including defense, intelligence, utilities, Natural Resources (i.e. Oil and Gas, Forestry ... etc.), social sciences, medicine and Public Safety (i.e. emergency management and criminology), disaster risk reduction and management (DRRM), and climate change adaptation (CCA). Spatial statistics typically result primarily from observation rather than experimentation. Hydrospatial is particularly used for the aquatic side and the members related to the water surface, column, bottom, sub-bottom and the coastal zones.

= = = = 基本应用 = = = 地理空间和水文空间分析，利用地理信息系统，是为解决环境和生命科学，特别是生态学、地质学和流行病学方面的问题而开发的。它已经扩展到几乎所有的行业，包括国防、情报、公用事业、自然资源(即。石油和天然气，林业..。等等。)、社会科学、医学及公共安全(即。应急管理和犯罪学) ，减少和管理灾害风险(DRRM) ，以及适应气候变化(CCA)。空间统计通常主要来自观察，而不是实验。水上空间特别适用于水面、水柱、水底、水底以及海岸带等与水面、水柱、水底有关的构件。

#### Basic operations

Vector-based GIS is typically related to operations such as map overlay (combining two or more maps or map layers according to predefined rules), simple buffering (identifying regions of a map within a specified distance of one or more features, such as towns, roads or rivers) and similar basic operations. This reflects (and is reflected in) the use of the term spatial analysis within the Open Geospatial Consortium (OGC) “simple feature specifications”. For raster-based GIS, widely used in the environmental sciences and remote sensing, this typically means a range of actions applied to the grid cells of one or more maps (or images) often involving filtering and/or algebraic operations (map algebra). These techniques involve processing one or more raster layers according to simple rules resulting in a new map layer, for example replacing each cell value with some combination of its neighbours’ values, or computing the sum or difference of specific attribute values for each grid cell in two matching raster datasets. Descriptive statistics, such as cell counts, means, variances, maxima, minima, cumulative values, frequencies and a number of other measures and distance computations are also often included in this generic term spatial analysis. Spatial analysis includes a large variety of statistical techniques (descriptive, exploratory, and explanatory statistics) that apply to data that vary spatially and which can vary over time. Some more advanced statistical techniques include Getis-ord Gi* or Anselin Local Moran's I which are used to determine clustering patterns of spatially referenced data.

Vector-based GIS is typically related to operations such as map overlay (combining two or more maps or map layers according to predefined rules), simple buffering (identifying regions of a map within a specified distance of one or more features, such as towns, roads or rivers) and similar basic operations. This reflects (and is reflected in) the use of the term spatial analysis within the Open Geospatial Consortium (OGC) “simple feature specifications”. For raster-based GIS, widely used in the environmental sciences and remote sensing, this typically means a range of actions applied to the grid cells of one or more maps (or images) often involving filtering and/or algebraic operations (map algebra). These techniques involve processing one or more raster layers according to simple rules resulting in a new map layer, for example replacing each cell value with some combination of its neighbours’ values, or computing the sum or difference of specific attribute values for each grid cell in two matching raster datasets. Descriptive statistics, such as cell counts, means, variances, maxima, minima, cumulative values, frequencies and a number of other measures and distance computations are also often included in this generic term spatial analysis. Spatial analysis includes a large variety of statistical techniques (descriptive, exploratory, and explanatory statistics) that apply to data that vary spatially and which can vary over time. Some more advanced statistical techniques include Getis-ord Gi* or Anselin Local Moran's I which are used to determine clustering patterns of spatially referenced data.

基于矢量的地理信息系统通常涉及地图叠加(根据预先确定的规则组合两个或两个以上的地图或地图层)、简单的缓冲(在一个或多个特征的特定距离内确定地图的区域，如城镇、道路或河流)和类似的基本业务。这反映了空间分析这个术语在开放地理空间协会标准中的使用，也反映了这一点。对于在环境科学和遥感中广泛使用的基于栅格的地理信息系统，这通常意味着对一个或多个地图(或图像)的网格单元采取一系列行动，通常涉及过滤和/或代数操作(地图代数)。这些技术包括根据简单的规则处理一个或多个栅格层，从而产生一个新的地图层，例如用邻近单元值的某种组合替换每个单元值，或计算两个匹配的栅格数据集中每个网格单元特定属性值的和或差。描述统计学，如细胞计数，平均值，方差，最大值，最小值，累积值，频率和一些其他措施和距离计算也经常包括在这个通用术语空间分析。空间分析包括大量各种各样的统计技术(描述性、探索性和解释性统计) ，这些技术适用于在空间上不同且随时间变化的数据。一些更先进的统计技术包括 Getis-ord Gi * 或 Anselin Local Moran 的 i，它们用于确定空间参考数据的聚类模式。

#### Advanced operations

Geospatial and Hydrospatial analysis goes beyond 2D and 3D mapping operations and spatial statistics. It is multi-dimensional and also temporal and includes:

- Surface analysis — in particular analysing the properties of physical surfaces, such as gradient, aspect and visibility, and analysing surface-like data “fields”;
- Network analysis — examining the properties of natural and man-made networks in order to understand the behaviour of flows within and around such networks; and locational analysis. GIS-based network analysis may be used to address a wide range of practical problems such as route selection and facility location (core topics in the field of operations research), and problems involving flows such as those found in Hydrospatial and hydrology and transportation research. In many instances location problems relate to networks and as such are addressed with tools designed for this purpose, but in others existing networks may have little or no relevance or may be impractical to incorporate within the modeling process. Problems that are not specifically network constrained, such as new road or pipeline routing, regional warehouse location, mobile phone mast positioning or the selection of rural community health care sites, may be effectively analysed (at least initially) without reference to existing physical networks. Locational analysis "in the plane" is also applicable where suitable network datasets are not available, or are too large or expensive to be utilised, or where the location algorithm is very complex or involves the examination or simulation of a very large number of alternative configurations.
- Geovisualization — the creation and manipulation of images, maps, diagrams, charts, 3D views and their associated tabular datasets. GIS packages increasingly provide a range of such tools, providing static or rotating views, draping images over 2.5D surface representations, providing animations and fly-throughs, dynamic linking and brushing and spatio-temporal visualisations. This latter class of tools is the least developed, reflecting in part the limited range of suitable compatible datasets and the limited set of analytical methods available, although this picture is changing rapidly. All these facilities augment the core tools utilised in spatial analysis throughout the analytical process (exploration of data, identification of patterns and relationships, construction of models, and communication of results)

Geospatial and Hydrospatial analysis goes beyond 2D and 3D mapping operations and spatial statistics. It is multi-dimensional and also temporal and includes:

- Surface analysis — in particular analysing the properties of physical surfaces, such as gradient, aspect and visibility, and analysing surface-like data “fields”;
- Network analysis — examining the properties of natural and man-made networks in order to understand the behaviour of flows within and around such networks; and locational analysis. GIS-based network analysis may be used to address a wide range of practical problems such as route selection and facility location (core topics in the field of operations research), and problems involving flows such as those found in Hydrospatial and hydrology and transportation research. In many instances location problems relate to networks and as such are addressed with tools designed for this purpose, but in others existing networks may have little or no relevance or may be impractical to incorporate within the modeling process. Problems that are not specifically network constrained, such as new road or pipeline routing, regional warehouse location, mobile phone mast positioning or the selection of rural community health care sites, may be effectively analysed (at least initially) without reference to existing physical networks. Locational analysis "in the plane" is also applicable where suitable network datasets are not available, or are too large or expensive to be utilised, or where the location algorithm is very complex or involves the examination or simulation of a very large number of alternative configurations.
- Geovisualization — the creation and manipulation of images, maps, diagrams, charts, 3D views and their associated tabular datasets. GIS packages increasingly provide a range of such tools, providing static or rotating views, draping images over 2.5D surface representations, providing animations and fly-throughs, dynamic linking and brushing and spatio-temporal visualisations. This latter class of tools is the least developed, reflecting in part the limited range of suitable compatible datasets and the limited set of analytical methods available, although this picture is changing rapidly. All these facilities augment the core tools utilised in spatial analysis throughout the analytical process (exploration of data, identification of patterns and relationships, construction of models, and communication of results)

= = = = 高级操作 = = = 地理空间和水文空间分析超越了二维和三维制图操作和空间统计。它是多维的，也是暂时的，包括:

- 表面分析ーー特别是分析物理表面的特性，例如梯度、方向和可见度，并分析表面类似的数据”场”;
- 网络分析ーー审查自然和人造网络的特性，以便了解这些网络内部和周围流动的行为; 以及定位分析。基于地理信息系统的网络分析可用于解决一系列实际问题，例如路线选择和设施选址(运筹学领域的核心课题) ，以及涉及流量的问题，例如在 Hydrospatial 发现的问题和水文及运输研究。在许多情况下，位置问题与网络有关，因此是通过为此目的设计的工具来解决的，但在其他情况下，现有的网络可能很少或根本没有相关性，或者可能不切实际，难以纳入建模过程。不受具体网络限制的问题，例如新的公路或管道路线、区域仓库位置、移动电话天线杆位置或农村社区保健站点的选择，可以在不参考现有物理网络的情况下进行有效分析(至少在初期是这样)。”平面上”的定位分析也适用于下列情况: 没有合适的网络数据集，或者数据集太大或太昂贵而无法使用，或者定位算法非常复杂，或者需要对大量备选配置进行检查或模拟。
- 地理数据可视化ー创建和操作图像、地图、图表、图表、3 d 视图及其相关表格数据集。GIS 软件包越来越多地提供一系列这样的工具，提供静态或旋转视图，在2.5 d 表面上绘制图像，提供动画和飞越，动态链接和刷新，以及时空可视化。后一类工具是最不发达的，部分反映了适当的兼容数据集的范围有限和现有的分析方法有限，尽管这种情况正在迅速改变。所有这些设施增强了在整个分析过程中(数据探索、模式和关系的识别、模型的构建和结果的交流)在空间分析中使用的核心工具

#### Mobile Geospatial and Hydrospatial Computing

Traditionally geospatial and hydrospatial computing has been performed primarily on personal computers (PCs) or servers. Due to the increasing capabilities of mobile devices, however, geospatial computing in mobile devices is a fast-growing trend.^{[40]} The portable nature of these devices, as well as the presence of useful sensors, such as Global Navigation Satellite System (GNSS) receivers and barometric pressure sensors, make them useful for capturing and processing geospatial and hydrospatial information in the field. In addition to the local processing of geospatial information on mobile devices, another growing trend is cloud-based geospatial computing. In this architecture, data can be collected in the field using mobile devices and then transmitted to cloud-based servers for further processing and ultimate storage. In a similar manner, geospatial and hydrospatial information can be made available to connected mobile devices via the cloud, allowing access to vast databases of geospatial and hydrospatial information anywhere where a wireless data connection is available.

Traditionally geospatial and hydrospatial computing has been performed primarily on personal computers (PCs) or servers. Due to the increasing capabilities of mobile devices, however, geospatial computing in mobile devices is a fast-growing trend. The portable nature of these devices, as well as the presence of useful sensors, such as Global Navigation Satellite System (GNSS) receivers and barometric pressure sensors, make them useful for capturing and processing geospatial and hydrospatial information in the field. In addition to the local processing of geospatial information on mobile devices, another growing trend is cloud-based geospatial computing. In this architecture, data can be collected in the field using mobile devices and then transmitted to cloud-based servers for further processing and ultimate storage. In a similar manner, geospatial and hydrospatial information can be made available to connected mobile devices via the cloud, allowing access to vast databases of geospatial and hydrospatial information anywhere where a wireless data connection is available.

= = = = 移动地理空间和水文空间计算传统上主要在个人计算机或服务器上进行地理空间和水文空间计算。然而，随着移动设备性能的不断提高，移动设备中的地理空间计算是一个快速增长的趋势。这些装置的便携性以及全球导航卫星系统接收器和大气压力传感器等有用传感器的存在，使其有助于在该领域捕获和处理地理空间和水文空间信息。除了在移动设备上对地理空间信息进行本地处理之外，另一个日益增长的趋势是基于云的地理空间计算。在这种体系结构中，可以使用移动设备在现场收集数据，然后将数据传输到基于云的服务器进行进一步处理和最终存储。同样，地理空间和水文空间信息可以通过云向连接的移动设备提供，允许在任何有无线数据连接的地方访问海量的地理空间和水文空间信息数据库。

### Geographic information science and spatial analysis 模板:Anchor

thumb|300px|This flow map of Napoleon's ill-fated march on Moscow is an early and celebrated example of geovisualization. It shows the army's direction as it traveled, the places the troops passed through, the size of the army as troops died from hunger and wounds, and the freezing temperatures they experienced.

= = = 地理信息科学与空间分析 = = = 拇指 | 300px | 这幅拿破仑在莫斯科行军的流动地图是早期著名的地理数据可视化。它显示了军队行进的方向，军队经过的地方，军队因饥饿和受伤而死亡的规模，以及他们所经历的冰冻温度。

Geographic information systems (GIS) and the underlying geographic information science that advances these technologies have a strong influence on spatial analysis. The increasing ability to capture and handle geographic data means that spatial analysis is occurring within increasingly data-rich environments. Geographic data capture systems include remotely sensed imagery, environmental monitoring systems such as intelligent transportation systems, and location-aware technologies such as mobile devices that can report location in near-real time. GIS provide platforms for managing these data, computing spatial relationships such as distance, connectivity and directional relationships between spatial units, and visualizing both the raw data and spatial analytic results within a cartographic context. Subtypes include:

Geographic information systems (GIS) and the underlying geographic information science that advances these technologies have a strong influence on spatial analysis. The increasing ability to capture and handle geographic data means that spatial analysis is occurring within increasingly data-rich environments. Geographic data capture systems include remotely sensed imagery, environmental monitoring systems such as intelligent transportation systems, and location-aware technologies such as mobile devices that can report location in near-real time. GIS provide platforms for managing these data, computing spatial relationships such as distance, connectivity and directional relationships between spatial units, and visualizing both the raw data and spatial analytic results within a cartographic context. Subtypes include:

地理信息系统(GIS)和促进这些技术的基础地理信息科学对空间分析有很大的影响。获取和处理地理数据的能力日益增强，这意味着空间分析正在数据日益丰富的环境中进行。地理数据采集系统包括遥感图像、智能交通系统等环境监测系统以及移动设备等位置感知技术，这些设备可以近实时报告位置。地理信息系统提供了管理这些数据的平台，计算空间关系，如空间单位之间的距离、连通性和方向关系，并在制图环境中将原始数据和空间分析结果可视化。子类型包括:

- Geovisualization (GVis) combines scientific visualization with digital cartography to support the exploration and analysis of geographic data and information, including the results of spatial analysis or simulation. GVis leverages the human orientation towards visual information processing in the exploration, analysis and communication of geographic data and information. In contrast with traditional cartography, GVis is typically three- or four-dimensional (the latter including time) and user-interactive.
- Geographic knowledge discovery (GKD) is the human-centered process of applying efficient computational tools for exploring massive spatial databases. GKD includes geographic data mining, but also encompasses related activities such as data selection, data cleaning and pre-processing, and interpretation of results. GVis can also serve a central role in the GKD process. GKD is based on the premise that massive databases contain interesting (valid, novel, useful and understandable) patterns that standard analytical techniques cannot find. GKD can serve as a hypothesis-generating process for spatial analysis, producing tentative patterns and relationships that should be confirmed using spatial analytical techniques.
- Spatial decision support systems (SDSS) take existing spatial data and use a variety of mathematical models to make projections into the future. This allows urban and regional planners to test intervention decisions prior to implementation.
^{[41]}

- Geovisualization (GVis) combines scientific visualization with digital cartography to support the exploration and analysis of geographic data and information, including the results of spatial analysis or simulation. GVis leverages the human orientation towards visual information processing in the exploration, analysis and communication of geographic data and information. In contrast with traditional cartography, GVis is typically three- or four-dimensional (the latter including time) and user-interactive.
- Geographic knowledge discovery (GKD) is the human-centered process of applying efficient computational tools for exploring massive spatial databases. GKD includes geographic data mining, but also encompasses related activities such as data selection, data cleaning and pre-processing, and interpretation of results. GVis can also serve a central role in the GKD process. GKD is based on the premise that massive databases contain interesting (valid, novel, useful and understandable) patterns that standard analytical techniques cannot find. GKD can serve as a hypothesis-generating process for spatial analysis, producing tentative patterns and relationships that should be confirmed using spatial analytical techniques.
- Spatial decision support systems (SDSS) take existing spatial data and use a variety of mathematical models to make projections into the future. This allows urban and regional planners to test intervention decisions prior to implementation.

- 地图地理数据可视化结合科学可视化和数码制图，以支援地理数据和资料的探索和分析，包括空间分析或模拟的结果。在地理数据和信息的探索、分析和交流中，GVis 利用了人类对视觉信息处理的导向。与传统制图相比，gvi 通常是三维或四维的(后者包括时间)和用户交互。地理知识发现(GKD)是以人为中心，应用高效的计算工具探索海量空间数据库的过程。GKD 包括地理数据挖掘，但也包括相关的活动，如数据选择，数据清理和预处理，以及结果的解释。GVis 也可以在 GKD 过程中发挥核心作用。GKD 是基于这样一个前提，即海量数据库包含标准分析技术无法找到的有趣(有效、新颖、有用和可理解的)模式。GKD 可以作为空间分析的假设生成过程，产生应用空间分析技术确认的初步模式和关系。
- 空间决策支援系统(SDSS)利用现有的空间数据，利用多种数学模型作出未来的预测。这使得城市和区域规划者能够在实施之前测试干预决策。

## See also

- General topics

- Buffer analysis
- Cartography
- Complete spatial randomness
- Cost distance analysis
- GeoComputation
- Geospatial intelligence
- Geospatial predictive modeling
- Dimensionally Extended nine-Intersection Model (DE-9IM)
- Geographic information science
- Mathematical statistics
- Modifiable areal unit problem
- Point process
- Proximity analysis
- Spatial autocorrelation
- Spatial descriptive statistics
- Spatial relation
- Terrain analysis
- List of spatial analysis software

- General topics

- Buffer analysis
- Cartography
- Complete spatial randomness
- Cost distance analysis
- GeoComputation
- Geospatial intelligence
- Geospatial predictive modeling
- Dimensionally Extended nine-Intersection Model (DE-9IM)
- Geographic information science
- Mathematical statistics
- Modifiable areal unit problem
- Point process
- Proximity analysis
- Spatial autocorrelation
- Spatial descriptive statistics
- Spatial relation
- Terrain analysis
- List of spatial analysis software

= = = = 一般主题

- 缓冲区分析
- 制图
- 完整的空间随机性
- 成本距离分析
- 地理计算
- 地理空间智能
- 地理空间预测建模
- 维度扩展的九交点模型(DE-9IM)
- 地理信息科学
- 数理统计
- 可调整地区单元问题
- 点过程
- 邻近分析
- 空间自相关
- 空间描述统计学
- 地形分析
- 空间分析软件列表

- Specific applications

- Specific applications

- Geographic information systems
- Geodemographic segmentation
- Viewshed analysis
- Fuzzy architectural spatial analysis
- Suitability analysis
- Extrapolation domain analysis
- Geoinformatics
- Geostatistics
- Boundary problem (in spatial analysis)
- Spatial epidemiology
- Spatial econometrics

地理信息系统

- 地理信息系统
- 地理人口分割
- Viewshed 分析
- 模糊建筑空间分析
- 适宜性分析
- 适宜性外推领域分析
- 地理信息学
- 地理统计学
- 边界问题(空间分析)
- 空间流行病学
- 空间计量学

## References

- ↑ The History of Land Surveying. Accessed Dec 17 2020. https://info.courthousedirect.com/blog/history-of-land-surveying
- ↑ Mark Monmonier
*How to Lie with Maps*University of Chicago Press, 1996. - ↑ Journel, A G and Huijbregts, C J,
*Mining Geostatistics*, Academic Press Inc, London. - ↑ Knegt, De; Coughenour, M.B.; Skidmore, A.K.; Heitkönig, I.M.A.; Knox, N.M.; Slotow, R.; Prins, H.H.T. (2010). "Spatial autocorrelation and the scaling of species–environment relationships".
*Ecology*.**91**(8): 2455–2465. doi:10.1890/09-1359.1. PMID 20836467. - ↑ "Spatial Association" (PDF). Geography Teachers' Association of Victoria. Retrieved 17 November 2014.
- ↑ Halley, J. M.; Hartley, S.; Kallimanis, A. S.; Kunin, W. E.; Lennon, J. J.; Sgardelis, S. P. (2004-03-01). "Uses and abuses of fractal methodology in ecology".
*Ecology Letters*(in English).**7**(3): 254–271. doi:10.1111/j.1461-0248.2004.00568.x. ISSN 1461-0248. - ↑ Ocaña-Riola, R (2010). "Common errors in disease mapping".
*Geospatial Health*.**4**(2): 139–154. doi:10.4081/gh.2010.196. PMID 20503184. - ↑ "Understanding Spatial Fallacies".
*The Learner's Guide to Geospatial Analysis*. Penn State Department of Geography. Retrieved 27 April 2018. - ↑ Quattrochi, Dale A (2016-02-01).
*Integrating scale in remote sensing and GIS*. ISBN 9781482218268. OCLC 973767077. - ↑ Robinson, Ws (April 2009). "Ecological Correlations and the Behavior of Individuals*".
*International Journal of Epidemiology*.**38**(2): 337–341. doi:10.1093/ije/dyn357. PMID 19179346. - ↑ Graham J. Upton & Bernard Fingelton:
**Spatial Data Analysis by Example Volume 1: Point Pattern and Quantitative Data**John Wiley & Sons, New York. 1985. - ↑ Harman H H (1960)
*Modern Factor Analysis*, University of Chicago Press - ↑ Rummel R J (1970)
*Applied Factor Analysis*. Evanston, ILL: Northwestern University Press. - ↑ Bell W & E Shevky (1955)
*Social Area Analysis*, Stanford University Press - ↑ Moser C A & W Scott (1961)
*British Towns ; A Statistical Study of their Social and Economic Differences*, Oliver & Boyd, London. - ↑ Berry B J & F Horton (1971)
*Geographic Perspectives on Urban Systems*, John Wiley, N-Y. - ↑ Berry B J & K B Smith eds (1972)
*City Classification Handbook : Methods and Applications*, John Wiley, N-Y. - ↑ Ciceri M-F (1974)
*Méthodes d’analyse multivariée dans la géographie anglo-saxonne*, Université de Paris-1 ; free download on http://www-ohp.univ-paris1.fr - ↑ Tucker L R (1964) « The extension of Factor Analysis to three-dimensional matrices », in Frederiksen N & H Gulliksen eds,
*Contributions to Mathematical Psychology*, Holt, Rinehart and Winston, NY. - ↑ R. Coppi & S. Bolasco, eds. (1989),
*Multiway data analysis*, Elsevier, Amsterdam. - ↑ Cant, R.G. (1971). "Changes in the location of manufacturing in New Zealand 1957-1968: An application of three-mode factor analysis".
*New Zealand Geographer*.**27**: 38–55. doi:10.1111/j.1745-7939.1971.tb00636.x. - ↑ Marchand B (1986)
*The Emergence of Los Angeles, 1940-1970*, Pion Ltd, London - ↑ Brunsdon, C.; Fotheringham, A.S.; Charlton, M.E. (1996). "Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity".
*Geographical Analysis*.**28**(4): 281–298. doi:10.1111/j.1538-4632.1996.tb00936.x. - ↑
^{24.0}^{24.1}Banerjee, Sudipto; Carlin, Bradley P.; Gelfand, Alan E. (2014),*Hierarchical Modeling and Analysis for Spatial Data, Second Edition*, Monographs on Statistics and Applied Probability (2nd ed.), Chapman and Hall/CRC, ISBN 9781439819173 - ↑ Bivand, Roger (20 January 2021). "CRAN Task View: Analysis of Spatial Data". Retrieved 21 January 2021.
- ↑ Banerjee, Sudipto; Gelfand, Alan E.; Finley, Andrew O.; Sang, Huiyan (2008). "Gaussian predictive process models for large spatial datasets".
*Journal of the Royal Statistical Society, Series B*.**70**(4): 825–848. doi:10.1111/j.1467-9868.2008.00663.x. PMC 2741335. PMID 19750209. - ↑ Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O.; Gelfand, Alan E. (2016). "Hierarchical Nearest Neighbor Gaussian Process Models for Large Geostatistical Datasets".
*Journal of the American Statistical Association*.**111**(514): 800–812. arXiv:1406.7343. doi:10.1080/01621459.2015.1044091. PMC 5927603. PMID 29720777. - ↑ Silva, E. A.; Clarke, K.C. (2002). "Calibration of the SLEUTH urban growth model for Lisbon and Porto, Portugal".
*Computers, Environment and Urban Systems*.**26**(6): 525–552. doi:10.1016/S0198-9715(01)00014-X. - ↑ Silva, E A (2003). "Complexity, emergence and cellular urban models: lessons learned from applying SLEUTH to two Portuguese metropolitan areas".
*European Planning Studies*.**13**(1): 93–115. doi:10.1080/0965431042000312424. S2CID 197257. - ↑ Liu and Silva (2017). "Examining the dynamics of the interaction between the development of creative industries and urban spatial structure by agent-based modelling: A case study of Nanjing, China".
*Urban Studies*.**65**(5): 113–125. doi:10.1177/0042098016686493. S2CID 157318972. - ↑ Liu, Lun; Silva, Elisabete A.; Wu, Chunyang; Wang, Hui (2017). "A machine learning-based method for the large-scale evaluation of the qualities of the urban environment" (PDF).
*Computers Environment and Urban Systems*.**65**: 113–125. doi:10.1016/j.compenvurbsys.2017.06.003. - ↑ Honarkhah, M; Caers, J (2010). "Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling".
*Mathematical Geosciences*.**42**(5): 487–517. doi:10.1007/s11004-010-9276-7. S2CID 73657847. - ↑ Tahmasebi, P.; Hezarkhani, A.; Sahimi, M. (2012). "Multiple-point geostatistical modeling based on the cross-correlation functions".
*Computational Geosciences*.**16**(3): 779–79742. doi:10.1007/s10596-012-9287-1. S2CID 62710397. - ↑ Tahmasebi, P.; Sahimi, M. (2015). "Reconstruction of nonstationary disordered materials and media: Watershed transform and cross-correlation function".
*Physical Review E*.**91**(3): 032401. Bibcode:2015PhRvE..91c2401T. doi:10.1103/PhysRevE.91.032401. PMID 25871117. - ↑ Tahmasebi, P.; Sahimi, M. (2015). "Geostatistical Simulation and Reconstruction of Porous Media by a Cross-Correlation Function and Integration of Hard and Soft Data".
*Transport in Porous Media*.**107**(3): 871–905. doi:10.1007/s11242-015-0471-3. S2CID 123432975. - ↑ "Graduate Program in Spatial Analysis".
*Ryerson University*. Ryerson University. Retrieved 17 December 2015. - ↑ geospatial. Collins English Dictionary - Complete & Unabridged 11th Edition. Retrieved 5tth August 2012 from CollinsDictionary.com website: http://www.collinsdictionary.com/dictionary/english/geospatial
- ↑ Dictionary.com's 21st Century Lexicon Copyright © 2003-2010 Dictionary.com, LLC http://dictionary.reference.com/browse/geospatial
- ↑ The geospatial web – blending physical and virtual spaces. -{zh-cn:互联网档案馆; zh-tw:網際網路檔案館; zh-hk:互聯網檔案館;}-的存檔，存档日期2011-10-02., Arno Scharl in receiver magazine, Autumn 2008
- ↑ Chen, Ruizhi; Guinness, Robert E. (2014).
*Geospatial Computing in Mobile Devices*(1st ed.). Norwood, MA: Artech House. pp. 228. ISBN 978-1-60807-565-2. http://www.artechhouse.com/International/Books/Geospatial-Computing-in-Mobile-Devices-2159.aspx. - ↑ González, Ainhoa; Donnelly, Alison; Jones, Mike; Chrysoulakis, Nektarios; Lopes, Myriam (2012). "A decision-support system for sustainable urban metabolism in Europe".
*Environmental Impact Assessment Review*.**38**: 109–119. doi:10.1016/j.eiar.2012.06.007.

## Further reading

- Abler, R., J. Adams, and P. Gould (1971)
*Spatial Organization–The Geographer's View of the World*, Englewood Cliffs, NJ: Prentice-Hall. - Anselin, L. (1995) "Local indicators of spatial association – LISA".
*Geographical Analysis*, 27, 93–115. - Awange, Joseph; Paláncz, Béla (2016).
*Geospatial Algebraic Computations, Theory and Applications, Third Edition*. New York: Springer. ISBN 978-3319254630. - Banerjee, Sudipto; Carlin, Bradley P.; Gelfand, Alan E. (2014),
*Hierarchical Modeling and Analysis for Spatial Data, Second Edition*, Monographs on Statistics and Applied Probability (2nd ed.), Chapman and Hall/CRC, ISBN 9781439819173 - Benenson, I. and P. M. Torrens. (2004).
*Geosimulation: Automata-Based Modeling of Urban Phenomena.*Wiley. - Fotheringham, A. S., C. Brunsdon and M. Charlton (2000)
*Quantitative Geography: Perspectives on Spatial Data Analysis*, Sage. - Fotheringham, A. S. and M. E. O'Kelly (1989)
*Spatial Interaction Models: Formulations and Applications*, Kluwer Academic - Fotheringham, A. S.; Rogerson, P. A. (1993). "GIS and spatial analytical problems".
*International Journal of Geographical Information Systems*.**7**: 3–19. doi:10.1080/02693799308901936. - Goodchild, M. F. (1987). "A spatial analytical perspective on geographical information systems".
*International Journal of Geographical Information Systems*.**1**(4): 327–44. doi:10.1080/02693798708927820. - MacEachren, A. M. and D. R. F. Taylor (eds.) (1994)
*Visualization in Modern Cartography*, Pergamon. - Levine, N. (2010).
*CrimeStat: A Spatial Statistics Program for the Analysis of Crime Incident Locations*. Version 3.3. Ned Levine & Associates, Houston, TX and the National Institute of Justice, Washington, DC. Ch. 1-17 + 2 update chapters - Miller, H. J. (2004). "Tobler's First Law and spatial analysis".
*Annals of the Association of American Geographers*.**94**(2): 284–289. doi:10.1111/j.1467-8306.2004.09402005.x. S2CID 19172678. - Miller, H. J. and J. Han (eds.) (2001)
*Geographic Data Mining and Knowledge Discovery*, Taylor and Francis. - O'Sullivan, D. and D. Unwin (2002)
*Geographic Information Analysis*, Wiley. - Parker, D. C.; Manson, S. M.; Janssen, M.A.; Hoffmann, M. J.; Deadman, P. (2003). "Multi-agent systems for the simulation of land-use and land-cover change: A review".
*Annals of the Association of American Geographers*.**93**(2): 314–337. CiteSeerX 10.1.1.109.1825. doi:10.1111/1467-8306.9302004. S2CID 130096094. - White, R.; Engelen, G. (1997). "Cellular automata as the basis of integrated dynamic regional modelling".
*Environment and Planning B: Planning and Design*.**24**(2): 235–246. doi:10.1068/b240235. S2CID 62516646. - Scheldeman, X.; van Zonneveld, M. (2010).
*Training Manual on Spatial Analysis of Plant Diversity and Distribution*. Bioversity International. http://www.bioversityinternational.org/index.php?id=244&tx_news_pi1%5Bnews%5D=1256&cHash=110ef499ad0d2d17abb48849909f1356. - Fisher MM, Leung Y (2001) Geocomputational Modelling: techniques and applications. Springer Verlag, Berlin
- Fotheringham, S; Clarke, G; Abrahart, B (1997). "Geocomputation and GIS".
*Transactions in GIS*.**2**(3): 199–200. doi:10.1111/j.1467-9671.1997.tb00010.x. - Openshaw S and Abrahart RJ (2000) GeoComputation. CRC Press
- Diappi Lidia (2004) Evolving Cities: Geocomputation in Territorial Planning. Ashgate, England
- Longley PA, Brooks SM, McDonnell R, Macmillan B (1998), Geocomputation, a primer. John Wiley and Sons, Chichester
- Ehlen, J; Caldwell, DR; Harding, S (2002). "GeoComputation: what is it?".
*Comput Environ and Urban Syst*.**26**(4): 257–265. doi:10.1016/s0198-9715(01)00047-3. - Gahegan, M (1999). "What is Geocomputation?".
*Transactions in GIS*.**3**(3): 203–206. doi:10.1111/1467-9671.00017. - Murgante B., Borruso G., Lapucci A. (2009) "Geocomputation and Urban Planning"
*Studies in Computational Intelligence*, Vol. 176. Springer-Verlag, Berlin. - Reis, José P.; Silva, Elisabete A.; Pinho, Paulo (2016). "Spatial metrics to study urban patterns in growing and shrinking cities".
*Urban Geography*.**37**(2): 246–271. doi:10.1080/02723638.2015.1096118. S2CID 62886095. - Papadimitriou, F. (2002). "Modelling indicators and indices of landscape complexity: An approach using G.I.S".
*Ecological Indicators*.**2**(1–2): 17–25. doi:10.1016/S1470-160X(02)00052-3. - Fischer M., Leung Y. (2010) "GeoComputational Modelling: Techniques and Applications" Advances in Spatial Science. Springer-Verlag, Berlin.
- Murgante B., Borruso G., Lapucci A. (2011) "Geocomputation, Sustainability and Environmental Planning"
*Studies in Computational Intelligence*, Vol. 348. Springer-Verlag, Berlin. - Tahmasebi, P.; Hezarkhani, A.; Sahimi, M. (2012). "Multiple-point geostatistical modeling based on the cross-correlation functions".
*Computational Geosciences*.**16**(3): 779–79742. doi:10.1007/s10596-012-9287-1. S2CID 62710397. - Geza, Tóth; Áron, Kincses; Zoltán, Nagy (2014).
*European Spatial Structure*. LAP LAMBERT Academic Publishing. doi:10.13140/2.1.1560.2247.

- Abler, R., J. Adams, and P. Gould (1971) Spatial Organization–The Geographer's View of the World, Englewood Cliffs, NJ: Prentice-Hall.
- Anselin, L. (1995) "Local indicators of spatial association – LISA". Geographical Analysis, 27, 93–115.
- Benenson, I. and P. M. Torrens. (2004). Geosimulation: Automata-Based Modeling of Urban Phenomena. Wiley.
- Fotheringham, A. S., C. Brunsdon and M. Charlton (2000) Quantitative Geography: Perspectives on Spatial Data Analysis, Sage.
- Fotheringham, A. S. and M. E. O'Kelly (1989) Spatial Interaction Models: Formulations and Applications, Kluwer Academic
- MacEachren, A. M. and D. R. F. Taylor (eds.) (1994) Visualization in Modern Cartography, Pergamon.
- Levine, N. (2010). CrimeStat: A Spatial Statistics Program for the Analysis of Crime Incident Locations. Version 3.3. Ned Levine & Associates, Houston, TX and the National Institute of Justice, Washington, DC. Ch. 1-17 + 2 update chapters
- Miller, H. J. and J. Han (eds.) (2001) Geographic Data Mining and Knowledge Discovery, Taylor and Francis.
- O'Sullivan, D. and D. Unwin (2002) Geographic Information Analysis, Wiley.
- Fisher MM, Leung Y (2001) Geocomputational Modelling: techniques and applications. Springer Verlag, Berlin
- Openshaw S and Abrahart RJ (2000) GeoComputation. CRC Press
- Diappi Lidia (2004) Evolving Cities: Geocomputation in Territorial Planning. Ashgate, England
- Longley PA, Brooks SM, McDonnell R, Macmillan B (1998), Geocomputation, a primer. John Wiley and Sons, Chichester
- Murgante B., Borruso G., Lapucci A. (2009) "Geocomputation and Urban Planning" Studies in Computational Intelligence, Vol. 176. Springer-Verlag, Berlin.
- Fischer M., Leung Y. (2010) "GeoComputational Modelling: Techniques and Applications" Advances in Spatial Science. Springer-Verlag, Berlin.
- Murgante B., Borruso G., Lapucci A. (2011) "Geocomputation, Sustainability and Environmental Planning" Studies in Computational Intelligence, Vol. 348. Springer-Verlag, Berlin.

空间组织-地理学家的世界观》 ，恩格尔伍德克利夫斯: Prentice-Hall。安塞林(1995)“空间关联的局部指标—— LISA”。地理分析，27,93-115。

- Benenson, I. and P. M. Torrens.(2004).地理模拟: 基于自动机的城市现象建模。威利。
- Fotheringham，A.s. ，c. Brunsdon and m. Charlton (2000) Quantitative Geography: Perspectives on Spatial Data Analysis，Sage.
- Fotheringham，A.s. 和 M.E.o’kelly (1989)空间相互作用模型: 公式和应用，Kluwer 学术
- MacEachren，A.m. 和 D.R.f. Taylor (合编)(1994)现代制图的可视化，Pergamon。
- Levine n. (2010).犯罪统计: 用于分析犯罪事件发生地点的空间统计程序。3.3版本。内德莱文联合公司，休斯顿，TX 和国家司法研究所，华盛顿特区。Ch.1-17 + 2更新章节
- 米勒，h. j. 和 j. 韩(合编)(2001)地理数据挖掘与知识发现，泰勒和弗朗西斯。
- o’sullivan，d. and d. Unwin (2002) Geographic Information Analysis，Wiley。
- Fisher MM，Leung y (2001)地球计算模型: 技术和应用。Spinger Verlag，Berlin
- Openshaw s and Abrahart RJ (2000) geocalculation.利迪亚(2004) : 国土规划中的地理计算。Ashgate, England

- Longley PA, Brooks SM, McDonnell R, Macmillan B (1998), Geocomputation, a primer.约翰 · 威利和儿子们，奇切斯特 · 莫甘特 b，博鲁索 g，拉普奇 a。(2009)“地理计算与城市规划”计算智能研究，第卷。176.Springer-Verlag, Berlin.

- Fischer M., Leung Y.(2010)「地球计算模型: 技术与应用」空间科学进展。Springer-Verlag, Berlin.
- Murgante b，Borruso g，laucci a.(2011)「地理计算、可持续发展与环境规划」研究。348.Springer-Verlag, Berlin.

## External links

模板:Library resources box 模板:Commons category

- ICA Commission on Geospatial Analysis and Modeling
- An educational resource about spatial statistics and geostatistics
- A comprehensive guide to principles, techniques & software tools
- Social and Spatial Inequalities
- National Center for Geographic Information and Analysis (NCGIA)
- International Cartographic Association (ICA), the world body for mapping and GIScience professionals

- ICA Commission on Geospatial Analysis and Modeling
- An educational resource about spatial statistics and geostatistics
- A comprehensive guide to principles, techniques & software tools
- Social and Spatial Inequalities
- National Center for Geographic Information and Analysis (NCGIA)
- International Cartographic Association (ICA), the world body for mapping and GIScience professionals

# = 外部链接 =

- ICA 地理空间分析和建模委员会
- 空间统计和地理统计学教育资源
- 原则、技术和软件工具综合指南
- 社会和空间不平等
- 国家地理信息和分析中心
- 国际制图协会，世界制图和地理信息系统专业人员机构

This page was moved from wikipedia:en:Spatial analysis. Its edit history can be viewed at 空间统计学/edithistory

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