Convergence between GIS and spatial statistics : What ? Where ? When ?

ion science technology computing Figure 1. The simplified process of getting informed decisions about the real world via model conceptualization and technological implementation. Around 1990, the recognition of the special characteristics of information processing with explicit referencing to location, commonly and briefly referred to as spatial data, lead two, previously relatively distinct areas to a crossroads. Geographical information systems (GIS), a term that had been coined (Tomlinson 1967) and loosely defined along with landor spatial information systems long before (Burrough 1986), became a focal point of research, education and markets as indicated by the foundation of national research centres on both sides of the Atlantic (Maguire et al., 1991). Spatial statistics, a term that had been also long defined with more rigour (Ripley 1981, Cliff and Ord 1981) but sometimes interchangeably with geostatistics (Journel and Huijbregts 1978), was started to be considered a stimulating unifying ground for mathematical statisticians as well as for practitioners (Cressie 1991). It may not be accidental that close to thousand page monographs were published in both fields in 1991, and that the very first research initiative of the National Center for Geographic Information and Analysis (NCGIA) was devoted to envision the trajectories of convergence (Goodchild and Gopal 1989). The primary expectation a decade ago was to get the ’appropriate’ statistical theory in action, that is, in simplistic terms, algorithms that can make processing millions of interrelated data elements feasible in realistic time. 2. "What? " Estimation, prediction and simulation in geographic context There have been literally dozens of monographs published during this decade about spatial statistics in a broad sense (see, for example, Haining 1990, Deutsch and Journel 1992, Fotheringham and Rogerson 1994, Bailey and Gatrell 1985). The typical approach is to organize the methodology according to spatial data models (e.g., points, lines, areas, surfaces); then, exploratory tools and measures are described, and finally, stochastic models are introduced. This approach may be the consequence of a belief that practitioners relate better to data than to models. Many quantitative geographical texts refer to "Everything is related to everything, but near things are more related than others" as the first law of geography (Tobler 1979), or even to "pattern generating processes" (Watt 1949). These could provide an excellent starting point to introduce stochastic models as related to observed and more likely versus less likely spatial patterns. Once the stochastic component of a disciplinary model is set up, estimation of model parameters, prediction of certain outcomes and simulation of equally likely realizations can be performed. These require practitioners to model spatial data, including spatial dependence, variance and uncertainty. Modelling spatial data eventually should lead to better practical understanding of the potential and the risks of particular methods. The better understanding of the nature of spatial statistical models has three potential advantages concerning the convergence with other disciplinary developments, particularly GIS. First, it will highlight the relationships between known processes in geography, ecology, environmental studies, soil science, socio-economic analysis, population studies, epidemiology, market research and any other field that may face large sets of problems with spatially dependent data. Therefore, it will assist decisions in applications about stationarity, order of neighbourhood structure, etc. Secondly, it will force practitioners to pay more attention to the careful selection of ’appropriate’ models. Presently, many practitioners are tempted to use simple measures and simple models to make data processing more tractable. A frequent consequence of this is that crucial expert knowledge about the pattern-process relationships are ignored or neglected. Therefore, thirdly, more challenging and more focused questions would be posed for statisticians (e.g., spatio-temporal models). 3. "Where? " Research, development, education, software It is our impression that some of the decade-old high expectations have not been met primarily because the ’point’ where the trajectories of GIS and spatial statistics converge is found too complicated. In spite of intensive research and development in fields applicable or closely related to spatial statistics, such as generalized linear models (McCullagh and Nelder 1989), information theory (Linhart and Zuchini 1986, Coifman and Wickerhauser 1992), wavelets (Daubechies 1992, Csillag and Kabos 1996), Markov chain Monte Carlo methods (Geman and Geman 1984, Raftery and Lewis 1992), practical demands, particularly in GIS applications often lack such depth. Whether one looks at, for example, public demand (e.g., environmental legislation), university courses (e.g., on geographical information processing), at publicly or commercially available standard data sets (e.g., digital elevation data, or census), or at trends in software development (e.g., the types of routines available for modelling spatial data within a GIS), all these seem to suggest that there may not be a ’quick fix’ for convergence. One of the obvious illustrative examples in spatial statistics is that ignoring spatial dependence results in ’undersampling’ and unwarrantedly optimistic confidence intervals in parameter estimation and prediction. Whether it is a prediction about acid-rain concentration, or the estimation of the parameters of a conditional autoregressive model of the market-share of a bank, results are typically reported as a single number without demonstrating and, in fact justifying, relaxing the assumption of independence in our sample. In summary, the convergence needs more support from education. The fact that some GIS software packages now have a ’magic’ button does not solve this problem. A very promising example is illustrated on Figure 2, where spatial data is shared by closely coupled software packages (S-PLUS 1998). With extra effort in educating people about the tradeoffs (i.e., more work leads to more reliable answers), the demand side is going to be transformed to stimulate change. Figure 2. An example of the present state-of-the-art closely-coupled software: ArcView and S-PLUS. Spatial data (e.g., points, lines, areas, surfaces) can be stored, analysed and visualised in ArcView. Spatial (and other) statistical analysis can be performed under the appropriate menu item running S-PLUS in tandem (i.e., without export/import). For example, neighbourhood topology can be stored and processed in both systems with ease. 4. "When? " The challenge of the next decade is uncertainty There is little doubt that the real question is not any longer ’why? ’ GIS and spatial statistics should be or are converging, but ’when? ’ they will converge. The more pressure there is going to be in decision-making to assess the uncertainty, of particular decisions the more intensively users will explore the promises and possibilities of linking GIS and spatial statistics. Currently, most applications of GIS and spatial statistics are not utilizing inherent disciplinary knowledge about the spatial distributions of phenomena. For example, when predictions based on soil properties are performed on a per-point basis or when market suitability is assessed locally for each enumeration area, most knowledge about spatial pattern is ignored which makes statistical confidence intervals too optimistic. More than likely, the wide availability of spatio-temporal data sets will significantly contribute to increasing the demand for rigourous uncertainty analysis. It appears that convergence between GIS and spatial statistics will happen when we all learn to live with uncertainty in our decisions rather than trying to hide or completely eliminate it.