Like all other academic disciplines, Geographic Information Science (GIScience) rests on a set of foundational ideas or principles on top of which all further work is based. These include Tobler’s First Law of Geography, conceptual models such as fields and objects, and the interplay of spatial heterogeneity and spatial dependency. While these foundations are often stable over long periods, revisiting and questioning them is essential as GIScience evolves with new insights and technologies from neighbouring disciplines. For instance, some of our foundational assumptions and everyday practices are from a time when the cost of computing was a limiting factor. Therefore, this dissertation seeks to rethink three widely accepted foundational principles of GIScience, namely pairs, direction, and geometry, to bridge the gap between the ever-changing landscape of technology, the broadening interest in spatial analytics across domains, and spatial thinking. More generally speaking, GIScience practice typically does not go beyond individual observations and pairs thereof. However, is direction truly about pairs, or is it higher-ordered? This dissertation will motivate the need for a geo-multipole, a new geographic conceptualization, as a direct extension of the geo-atom and geo-dipole that simultaneously considers observations of more than two locations. It will then apply the geo-multipole to ask whether direction was not overlooked in the original formulation of Tobler’s First Law. Finally, we will discuss how thinking in binary predicates in graph-based representations of geographic information has hindered the inclusion of qualitative higher-order relations such as betweenness.

Spatially explicit impact assessment analyses such as vulnerability studies often require spatially detailed population distribution as input. Downscaled population datasets otherwise known as disaggregated, gridded or fine resolution population datasets are becoming increasingly available at global and regional scales and are based on information from various sources with varying spatial and temporal resolutions as well as reliabilities. Uncertainty is endemic in such downscaled population estimates, particularly in developing countries yet it is hardly assessed. Consequently, decision-makers are potentially faced with a bias problem whereby uncertainties are masked and estimates are presented as unique or expected values even after being derived in a probabilistic context. This research explores how HIV prevalence in three districts of the United Republic of Tanzania might vary with the utilization of simulations of downscaled population estimates. In so doing, this study explores some scenarios in which HIV prevalence that corresponds to minimum expected cost of antiretroviral (ARV) treatment is estimated under three different decision-making attitudes, namely minimax regret, maximin and maximax, followed by a discussion of some implications of any variation in best estimates of HIV prevalence corresponding to the least impact on ARV cost.

Our findings show that for effective decision analysis, rather than using coarse aggregated values such as census data at the district level, decision-makers may benefit from the application of multiple simulated spatial distributions of fine scale population along with the associated ARV cost estimates. From this distribution of ARV cost estimates, decision-makers could select best estimates based on an explication of risk attitude, thus avoiding unforeseeable consequences of underestimating or overestimating impact assessment outcomes of HIV prevalence.