Statistical perspectives on geographic information science

Statistical geometry applies probabilistic methods to geometric forms. In the early days of the quantitative revolution statistical geometry appeared to provide a useful framework for geographic research, but its value appeared to decline in the 1970s and 1980s. Geographic information science (GIScience) addresses the fundamental issues underlying the geographic information technologies, and statistical geometry has proven valuable in a number of respects. Several classical results from statistical geometry are useful in the design of geographic information systems, and in understanding and modeling uncertainty in geographic information, and several statistical principles are observed to be generally applicable to geographic information. Modeling uncertainty in area-class maps has proven particularly difficult, and seven possible models are discussed. Statistical geometry provides an important link between the early work of the quantitative revolution in geography and modern research in GIScience.