Multiple scale pattern recognition and the foundation of observation-free statistics
This presentation lays the foundation of "observation-free" statistics, which is an approach that examines the sensitivity of measurements to variation in the definition of the observational unit. There is no single natural observational unit for the study of landscapes, while the selection of the observational unit (e.g. the pixel) can have tremendous influence on the analysis. This paper develops statistical measures to quantify how statistical results are influenced by various selections of the observational unit and various changes in scale. Specifically, this paper presents a statistical method to compare two maps that show different patterns of the same real variable. The technique budgets the agreement and disagreement between the maps in terms of components of the quantity (i.e. overall average) and the location (i.e. spatial arrangement) of the variable. The analysis computes the root mean square error (RMSE) and the mean absolute error (MAE) at multiple resolutions in order to detect the scales at which patterns are similar. The method allows the scientist to distinguish patterns associated with the landscape versus patterns due to artifacts of the format of the data. The procedure measures the most important ways in which two patterns compare in a manner consistent with an intuitive visual assessment. An example shows how the procedure is useful to measure the accuracy of a prediction of vegetation change in Africa.
American Society for Photogrammetry and Remote Sensing - Annual Conference 2005 - Geospatial Goes Global: From Your Neighborhood to the Whole Planet
MAE, pattern, resolution, RMSE, scale
Pontius, Robert Gilmore; Chen, Hao; and Thontteh, Olufunmilayo, "Multiple scale pattern recognition and the foundation of observation-free statistics" (2005). Geography. 779.