The geographic information system (GIS) provides an "anchor" of good database tools, and map drawing facilties, for spatially referenced data. We use this to select, or do simple manipulation of the data, and provide sophisticated maps of the spatial domain. The GIS is important also for maintaining the frame of reference to the data - a good map provides context for the data, which can otherwise get lost in statistical modeling and graphics.
A statistical analysis system (for example, S-Plus, SAS, XploRe, XLispStat, DataDesk) is used for modeling the trends and spatial dependence.
A visualization system (eg XGobi, DataDesk, XLispStat, XmdvTool, cdv) provides quick exploratory analysis and diagnostic checking for the model. The graphics need to be interactive, with several facilties for linked brushing, and dynamic to rotate the data through high-dimensional space. We should be able to quickly examine spatial dependence plots, models and residuals, as well as the multiple raw variables. We have a fairly broad variety of tools for extracting patterns in multivariate data. There needs to be a lot more research on the types of plots that can extract multivariate spatial trends and dependence. There are variogram clouds and cross-variogram clouds, which give information on individual and pairwise spatial dependence. But pairwise analysis of high-dimensional data is inadequate, so we suspect we will find that pairwise analysis of spatial dependence will be inadequate. So we need to devise new approaches to visually exploring spatial dependence amongst several variables.
All three systems need to be seamlessly linked. The scatterplot needs to be linked to the GIS map - brushing in the scatterplot should instantaneously update the map view and brushing in the map view should instantaneously update the scatterplot. We should be able to display the model overlaid on the geographic domain, and toggle between the model and residual surface. We should be able to calculate local statistics and make plots of these linked to the map.
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