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

The impetus for Cliff and Ord's landmark article, “The Problem of Spatial Autocorrelation,” was to avoid the problem of topological invariance in the spatial weights matrix. The problem and three points of view on it – theoretical, topological, and empirical – are discussed. [ABSTRACT FROM AUTHOR]

Despite criminology's widespread application of geography, the full implications of Cliff and Ord's article have yet to be realized. In this essay the major types of spatial studies in criminology are outlined, followed by a depiction of the context of criminological research at the time the article was published. Next the major changes to the field occurring after the publication of Cliff and Ord's paper, focusing on technology advances and theory, are set out. Fortunately these changes mean the discipline is well placed to move beyond seeing the presence of spatial autocorrelation as a methodological issue that needs to be explained away. [ABSTRACT FROM AUTHOR]

Spatial autocorrelation is a concept that helps to define the field of spatial analysis. It is central to studies using spatial statistics and spatial econometrics. In this paper, we trace the early development of the concept and explain the academic links that brought the concept to the fore in the late 1960s. In geography, the importance of the work of Michael F. Dacey, Andrew D. Cliff, and J. Keith Ord is emphasized. Later, with the publication of a volume on spatial econometrics by Luc Anselin, spatial research and the use of the concept of spatial autocorrelation received a considerable boost. These developments are outlined together with comments about recent and possible future trends in spatial autocorrelation-based research. [ABSTRACT FROM AUTHOR]

The author discusses how the 1969 article "The Problem of Spatial Autocorrelation," by A. Cliff and J. Ord has affected general science and theoretical geography. He claims that the 1969 article was not that successful in promoting the use of nonbinary geographic weights, but was successful in advocating the spatial autocorrelation indices. The author expresses his disappointment that no analytical spatial autocorrelation results have been developed for nonnormal random variables.