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This year is the 50th anniversary of Besag's classic auto‐models publication, a cornerstone in the development of modern‐day spatial statistics/econometrics. Besag struggled for nearly two decades to make his conceptualization collectively successful across a wide suite of random variables. But only his auto‐normal, and to a lesser degree his auto‐logistic/binomial, were workable. Others, like his auto‐Poisson, were effectively failures, whereas still others, such as potentials like an auto‐Weibull, defied even awkward mathematical incorporations of spatial lag terms. Besag circumvented this impediment by introducing an auto‐normal random effects components (within a Bayesian estimation context), building upon his single total success. This article describes an alternative approach, partly paralleling his reformulation while avoiding inserting spatial lag terms directly into probability density/mass functions, implanting spatial autocorrelation into cumulative distributions functions (CDFs), instead, via a spatially autocorrelated uniform distribution. The already existing probability integral transform and quantile function mathematical statistics theorems enable this mechanism to spatialize any random variable, with these new ones labeled sui‐models. [ABSTRACT FROM AUTHOR]

Except for about a half dozen papers, virtually all (co)authored by Griffith, the existing literature lacks much content about the interface between spatial optimization, a popular form of geographic analysis, and spatial autocorrelation, a fundamental property of georeferenced data. The popular p‐median location‐allocation problem highlights this situation: the empirical geographic distribution of demand virtually always exhibits positive spatial autocorrelation. This property of geospatial data offers additional overlooked information for solving such spatial optimization problems when it actually relates to their solutions. With a proof‐of‐concept outlook, this paper articulates connections between the well‐known Majority Theorem of the 1‐median minisum problem and local indices of spatial autocorrelation; the LISA statistics appear to be the more useful of these later statistics because they better embrace negative spatial autocorrelation. The relationship articulation outlined here results in the positing of a new proposition labeled the egalitarian theorem. [ABSTRACT FROM AUTHOR]

This study discusses the importance of balancing spatial and non‐spatial variation in spatial regression modeling. Unlike spatially varying coefficients (SVC) modeling, which is popular in spatial statistics, non‐spatially varying coefficients (NVC) modeling has largely been unexplored in spatial fields. Nevertheless, as we will explain, consideration of non‐spatial variation is needed not only to improve model accuracy but also to reduce spurious correlation among varying coefficients, which is a major problem in SVC modeling. We consider a Moran eigenvector approach modeling spatially and non‐spatially varying coefficients (S&NVC). A Monte Carlo simulation experiment comparing our S&NVC model with existing SVC models suggests both modeling accuracy and computational efficiency for our approach. Beyond that, somewhat surprisingly, our approach identifies true and spurious correlations among coefficients nearly perfectly, even when usual SVC models suffer from severe spurious correlations. It implies that S&NVC model should be used even when the analysis purpose is modeling SVCs. Finally, our S&NVC model is employed to analyze a residential land price data set. Its results suggest existence of both spatial and non‐spatial variation in regression coefficients in practice. The S&NVC model is now implemented in the R package spmoran. [ABSTRACT FROM AUTHOR]

When Spatial Analysis was published in 1968, it drew together the fruits of the first decade of geography's quantitative revolution. In the decades that have followed, quantitative geography has both [...]

The Poisson model, discovered nearly two centuries ago, is the basis for analyses of rare events. Its first applications included descriptions of deaths from mule kicks. More than half a [...]

The auto-Poisson probability model furnishes an obvious tool for modeling counts of geographically distributed rare events. Unfortunately, its original specification can accommodate only negative spatial autocorrelation, which itself is a [...]

One approach to dealing with spatial autocorrelation in regression analysis involves the filtering of variables in order to separate spatial effects from the variables' total effects. In this paper we [...]

Cliff and Ord (1969) published "The Problem of Spatial Autocorrelation," which established the foundation for their pioneering book entitled Spatial Autocorrelation (1973), whose revised edition appeared as Spatial Processes: Models [...]

This paper expands upon a GA 50thAnniversary panel presentation made at the 2018 New Orleans American Association of Geographers meeting. It notes that retrospectives for this topic already exist, both in terms of the journal and the sub‐discipline. This paper presents discussion about the following selected prominent transitional themes bridging the past and the future of geographical analysis: space–time data; geographic uncertainty and error; and, dimensional reduction spatial statistical modeling. It also presents discussion about the following three themes that are expected to receive considerable future attention: negative spatial autocorrelation; synergies between spatial statistics and spatial optimization; and, big spatial data. The first two of these topics essentially have been ignored in the literature to date. [ABSTRACT FROM AUTHOR]

Eigenvector spatial filtering (ESF) is a spatial modeling approach, which has been applied in urban and regional studies, ecological studies, and so on. However, it is computationally demanding, and may not be suitable for large data modeling. The objective of this study is developing fast ESF and random effects ESF (RE‐ESF), which are capable of handling very large samples. To achieve it, we accelerate eigen‐decomposition and parameter estimation, which make ESF and RE‐ESF slow. The former is accelerated by utilizing the Nyström extension, whereas the latter is by small matrix tricks. The resulting fast ESF and fast RE‐ESF are compared with nonapproximated ESF and RE‐ESF in Monte Carlo simulation experiments. The result shows that, while ESF and RE‐ESF are slow for several thousand samples, fast ESF and RE‐ESF require only several seconds for the samples. It is also suggested that the proposed approaches effectively remove positive spatial dependence in the residuals with very small approximation errors when the number of eigenvectors considered is 200 or more. Note that these approaches cannot deal with negative spatial dependence. The proposed approaches are implemented in an R package "spmoran." [ABSTRACT FROM AUTHOR]

With this issue, I am truly honored to assume the challenging duties of the ninth editor of the journal as it enters its 40th year of publication. I am pleased [...]

The Poisson distribution, first reported in print by Simeon-Denis Poisson in 1837, describes the probability that a random event will occur in a time or space interval under the conditions [...]

Geographical Analysis ( GA), in cooperation with the Wiley- Blackwell publishing business, undertook a project to complete the digitizing of all back issues of the journal and make those for the period 1969-2001 free to the academic community; the volumes for 2002-2005 already were, and continue to be, free. This article commemorates the completion of this event late in 2010, drawing upon this new resource to highlight important contributions made through the journal to the geography and spatial sciences community. Besides summarizing publication trends for the journal, in the tradition of Fenneman's Venn diagram conceptualization of overlaps between geography and its cognate disciplines, this article highlights prominent articles published in the journal that contributed to the four themes of urban and economic geography, transportation geography, spatial statistics, and geographic information science. Geographical Analysis (GA) en cooperación con publicaciones Wiley-Blackwell llevo a cabo el proyecto de digitación de todos los números pasados de la revista, los cuales están ahora a disposición de la comunidad académica sin costo alguno; los volúmenes de los años 2000-5 ya estaban disponibles y continúan siendo gratis. El presente artículo conmemora la culminación de dicho evento a fines de 2010, recogiendo los aportes de esta nueva fuente de información y resaltando varias contribuciones importantes hechas vía GA a la comunidad de geografía y ciencias espaciales. Además de resumir las tendencia de las publicaciones de la revista, en la tradición de la conceptualización de traslapes entre la geografía y disciplinas afines de los diagramas Venn Fanneman, el presente artículo resalta, artículos prominentes publicados en GA que contribuyeron a los cuatro temas principales: geografía urbana y económica, geografía del transporte, estadística especial y ciencias (sistemas) de información geográfica. 地理分析（GA）和Wiley-Blackwell出版商合作完成了对本刊1969-2001年所有刊册数字化的项目，并向学术界免费开放。事实上，从2002年第5卷就已经开始并将一直持续免费。本文记述了2010年末完成的这一事件，并依托这一新的数据资源，重新回顾了本刊对地理学和空间科学研究群体做出的重要贡献。本文总结了本刊论文发表趋势，从Fenneman的韦恩图概念传统来看是地理学及其相关学科的交叉。此外还回顾了本刊发表的对城市与经济地理、交通地理、空间统计以及地理信息科学方法做出卓越贡献的论文。 [ABSTRACT FROM AUTHOR]

An introduction to articles published within the issue is presented, including historical features relating to the new network science, two articles on the colored bridges problem and the geography of mathematics research collaboration and another article which discusses selected properties of eigenfunctions of graph adjancy matrices.