Toward a Theory of Spatial Statistics: Another Step Forward

An update is presented to an earlier piece outlining some steps that needed to be taken toward the establishment of a theory of spatial statistics. Findings that have appeared since this first paper are summarized and interpreted, and extensions and suggestions are offered for the further establishment of a basis for a theory of spatial statistics. Topics include boundary considerations, the role of latent spatial dependencies, and small-sample-size issues. These topics embrace the problems of data transformations, edge effect bias, reference sampling distributions, multivariate autocorrelation models, conditional expectations, and higher-order autoregressive structures. In part, a course is charted for the next step to be taken.     

Towards a Theory of Cultural Evolution

Abstract

Previous experience in the development of the mathematical theory of biological evolution, has helped the authors toward their theory of cultural evolution. In this review a constant comparison between the two evolutions, in both directions, has led to an interdisciplinary understanding. Cultural transmission is discussed in detail and the ten major modes of transmission are enunciated; cultural traits are defined and the variance within, as well as between, groups considered. Cultural and environmental selection as well as complex transmission are further aspects leading the authors to the conclusion, that in spite of gross oversimplification, their theory is essential for a rigorous qualitative investigation of cultural evolution.     

Intensities of Feeling: Towards a Spatial Politics of Affect

Abstract This paper attempts to take the politics of affect as not just incidental but central to the life of cities, given that cities are thought of as inhuman or transhuman entities and that politics is understood as a process of community without unity. It is in three main parts. The first part sets out the main approaches to affect that conform with this approach. The second part considers the ways in which the systematic engineering of affect has become central to the political life of Euro‐American cities, and why. The third part then sets out the different kinds of progressive politics that might become possible once affect is taken into account. There are some brief conclusions.     

"The Problem of Spatial Autocorrelation" and Local Spatial Statistics

This article examines the relationship between spatial dependency and spatial heterogeneity, two properties unique to spatial data. The property of spatial dependence has led to a large body of research into spatial autocorrelation and also, largely independently, into geostatistics. The property of spatial heterogeneity has led to a growing awareness of the limitation of global statistics and the value of local statistics and local statistical models. The article concludes with a discussion of how the two properties can be accommodated within the same modelling framework.     

基于ESDA的新疆旅游经济发展空间分异规律研究

在ArcGIS空间分析技术支持下,借助GeoDA空间自相关分析方法,以新疆85个县(市)旅游总收入及其空间差异为研究对象,分析新疆旅游经济发展空间分异格局,并用地学统计方法研究其空间分异规律,得出:(1)新疆旅游经济具有较强的空间依赖性,全局空间自相关特征明显,表现为集聚度高、异质性强、差异性大的空间极化分异态势;(2)局部上则表现为高高相聚和低低相随的两极分化格局,热点区以乌鲁木齐为中心,以昌吉州和吐鲁番、阿勒泰地区为延伸,沿交通网络向周边地区递减的空间分异格局,喀什、和田地区为冷点区;(3)交通可达性及旅游基础设施数量对新疆旅游经济发展起决定性作用,高速公路尤其是铁路对旅游经济影响最大;旅游资源优势度对旅游实现更加重要;交通区位对新疆旅游经济空间分异起着基础性作用.     

The Analysis of Spatial Association by Use of Distance Statistics

Introduced in this paper is a family of statistics, G, that can be used as a measure of spatial association in a number of circumstances. The basic statistic is derived, its properties are identified, and its advantages explained. Several of the G statistics make it possible to evaluate the spatial association of a variable within a specified distance of a single point. A comparison is made between a general G statistic and Moran's I for similar hypothetical and empirical conditions. The empirical work includes studies of sudden infant death syndrome by county in North Carolina and dwelling unit prices in metropolitan San Diego by zip-code districts. Results indicate that G statistics should be used in conjunction with I in order to identify characteristics of patterns not revealed by the I statistic alone and, specifically, the G_i and G_i* statistics enable us to detect local “pockets” of dependence that may not show up when using global statistics.     

Towards a Framework for Cooperation: Spatial Public Diplomacy on the Island of Ireland

Abstract

European spatial planning arguments advocate a blend of strategic thinking, coordination and related initiatives to promote and secure territorial cohesion. These ambitions embrace a set of normative agendas around economic, social and environmental convergence, competitiveness, policy coordination and efficient infrastructure provision across space. In practice, territorial management then involves devising interventions across inter-connecting scales of governance which comprise complex agency relations, differentiated places and defined communities. In transnational contexts, attempts to foster appropriate spatial governance arrangements and relations across sovereign borders necessitate re-crafting planning and development cultures and service delivery practices to advance territorial cohesion. Transnational working necessarily involves cooperation across an extended range of institutions, interests, influences and potential actors. This paper examines attempts to secure bi-lateral commitment to a joint planning framework for the two distinct territories on the island of Ireland. Specifically, it traces the formal and informal activities involved in the development of the 2013 Framework for Cooperation between the Republic of Ireland and Northern Ireland. Informed by ideas of cross-border regionalism, it discusses the necessary spatial public diplomacy involved in the social reconstruction of strategic spatial planning to improve policy coordination and cross-border working.     

Local Spatial Autocorrelation Statistics: Distributional Issues and an Application

The statistics G_i(d) and G_i*(d), introduced in Getis and Ord (1992) for the study of local pattern in spatial data, are extended and their properties further explored. In particular, nonbinary weights are allowed and the statistics are related to Moran's autocorrelation statistic, I. The correlations between nearby values of the statistics are derived and verified by simulation. A Bonferroni criterion is used to approximate significance levels when testing extreme values from the set of statistics. An example of the use of the statistics is given using spatial-temporal data on the AIDS epidemic centering on San Francisco. Results indicate that in recent years the disease is intensifying in the counties surrounding the city.     

Large Sample-Size Distribution of Statistics Used In Testing for Spatial Correlation

Test statistics for testing for spatial correlation in continuous variables have been given by both Moran and Geary and have subsequently been generalized. It has been conjectured for a long time that under the hypothesis of no spatial correlations all these statistics are normally distributed when the sample size is large. This paper proves a very general theorem on the large sample normality of quadratic forms. As corollaries to the theorem the asymptotic normality, under the hypothesis, of all the above-mentioned statistics is established. The necessary conditions are quite unrestrictive. It is also shown, by means of a counter example, that the conditions given in a similar theorem (Cliff and Ord) are inadequate to ensure normality.     

A Programming Approach to Minimizing and Maximizing Spatial Autocorrelation Statistics

A programming approach is presented for identifying the form of the weights matrix W which either minimizes or maximizes the value of Moran's spatial autocorrelation statistic for a specified vector of data values. Both nonlinear and linear programming solutions are presented. The former are necessary when the sum of the links in W is unspecified while the latter can be used if this sum is fixed. The approach is illustrated using data examined in previous studies for two variables measured for the counties of Eire. While programming solutions involving different sets of constraints are derived, all yield solutions in which the number of nonzero elements in W is considerably smaller than that in W defined using the contiguity relationships between the counties. In graph theory terms, all of the Ws derived define multicomponent graphs. Other characteristics of the derived Ws are also presented.     

Spatial Autocorrelation Statistics of Areal Prevalence Rates under High Uncertainty in Denominator Data

We propose a new estimator of spatial autocorrelation of areal incidence or prevalence rates in small areas, such as crime and health indicators, for correcting spatially heterogeneous sampling errors in denominator data. The approach is dubbed the heteroscedasticity‐consistent empirical Bayes (HC‐EB) method. As American Community Survey (ACS) data have been released to the public for small census geographies, small‐area estimates now form the demographic landscape of neighborhoods. Meanwhile, there is growing awareness of the diminished statistical validity of global and local Moran’s I when such small‐area estimates are used in denominator data. Using teen birth rates by census tracts in Mecklenburg County, North Carolina, we present comparisons of conventional and new HC‐EB estimates of Global and Local Moran’s I statistics created on ACS data, along with estimates on ground truth values from the 2010 decennial census. Results show that the new adjustment method dramatically enhances the statistical validity of global and local spatial autocorrelation statistics.