Graphical tools for conditional probabilistic exploration of multivariate spatial datasets

Abstract

Two exploratory data analysis techniques the comap and the quad plot are shown to have both strengths and shortcomings when analysing spatial multivariate datasets. A hybrid of these two techniques is proposed: the quad map which is shown to overcome the outlined shortcomings when applied to a dataset containing weather information for disaggregate incidents of urban fires. Common to the quad plot, the quad map uses Polya models in order to articulate the underlying assumptions behind histograms. The Polya model formalises the situation in which past fire incident counts are computed and displayed in (multidimensional) histograms as appropriate assessments of conditional probability providing valuable diagnostics such as posterior variance i.e. sensitivity to new information. Finally we discuss how new technology in particular Online Analytics Processing (OLAP) and Geographical Information Systems (GISs) offer potential in automating exploratory spatial data analyses techniques, such as the quad map.