A Multiscale Framework for Spatial Modeling in Geography

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Scale dependency is an inherent property of geographic phenomena, and the increasingly pressing importance of better understanding the effects of scale has been highlighted in a number of recent public forums. So-called multiscale models can be particularly appropriate for this task, that is, mathematical/statistical models in which the overall structure of an object under study is decomposed according to its component structures at different scales of spatial and/or temporal resolution. In this project, work will focus on the development and implementation of a multiscale statistical modeling framework recently introduced by the principal investigators specifically for geographic data structures. The framework underlying these models is that of a set of hierarchically defined partitions (or aggregations) of a data space. The effects of scale are captured through a fundamental decomposition (or factorization) of the data likelihood, induced by this hierarchy, into individual components of local information at all possible spatial resolutions. Upon combining these multiscale likelihoods with an appropriately defined Bayesian prior probability structure, a powerful inferential framework results. The specific aims of this project are three-fold: (i) further develop and extend the original, general modeling structure, so as to (ii) tailor it to two specific class of problems in geographical analysis, those of remote sensing and census geography, and finally (iii) produce formal tools of statistical inference for characterizing the influence of scale effects in standard tasks such as prediction, classification, knowledge discovery, and decision making.Broadly speaking, this research is aimed at fully developing an inferential statistical framework for the study of scale effects in geographic phenomena, with particular emphasis on problems in remote sensing and census geography. As such, it is expected to have implications in areas such as geographical theory, knowledge discovery and spatial data mining, and theory and methods for database generalization. The resulting framework will be sufficiently flexible and computationally efficient to allow for integration into geographic information systems (GIS), such as those arising in the context of environmental, epidemiological, and agricultural applications.