The relationships between knowledge, especially conceptual knowledge, scientific disciplines, and empirical observations are often far from simple. Insight and intuition play an important role in leading to new conclusions. A striking example of the significance of location in such intuition is the mapping of the locations of cholera deaths in London in 1854 by Dr John Snow, indicating that proximity to the Broad Street water pump could be important. By disabling the pump, Dr Snow ended the epidemic (cf. Tufte, 1997). Few of us will be able to make such dramatic interventions just by mapping our data, but where data are located at geographical coordinates, it seems unfortunate not to examine the possibility that local dependence may be part of the story.
Spatial statistics span many disciplines, with methods varying in relation to the specific research questions being addressed, whether predicting ore quality in mining, examining suspiciously high frequencies of disease events, or handling the vast data volumes being generated by GPS (global positioning system) and satellite remote sensing. A unique feature of spatial data is that geographical location provides a key shared either exactly or approximately between data sets of different origins. Census data can be overlayed over patient or customer data; environmental data can be integrated with disease frequencies; problems which hitherto did not admit ready empirical testing are becoming approachable. Geographical information systems are contributing to the development and spread of spatial statistical methods, which have, largely since their inception, remained within narrow research confines, at least partly because they were seen as being computationally burdensome.
In this review, I will concentrate on indicating the kinds of research problems to which spatial statistical methods can be applied, with particular reference to trade and location where possible. It should be admitted that the number of such applications is as yet very limited, but this does not appear to be because there are no opportunities -- rather it seems that Krugman's argument about lack of mutual acquaintance also applies here (1995). Further, few of the econometric tools economists are furnished with provide suitable estimation methods. Haining (1990) gives a broad general introduction to the field, supplemented by Hepple (1996) and Getis and Ord (1996). Three recent surveys, including available software, are Levine (1996), Gatrell and Bailey (1996), and Bivand (forthcoming).
Having examined research traditions in trade and location in relation to the testing of models against empirical observations, basic issues in spatial statistics will be discussed, focusing on how the relationships between locations are expressed. We move next to the analysis of point patterns and fields. Most of the paper deals with lattice data typical of social science research problems. Starting from the exploratory analysis of spatial data -- also a vital stage in point pattern analysis and geostatistics, global measures of spatial association are presented before the most recent work on local indicators is reviewed. Attention is also drawn to the modifiable areal unit problem often present in the analysis of lattice data. Finally, we turn to spatial econometrics, firstly the detection of spatial dependency in estimation results based on the assumption that the mutual location of observations is without importance, and secondly the explicit modelling of this dependence. This section is concluded by a discussion of a method of geographical weighting, providing a way of revealing non-stationarity in spatial data under analysis.