A Multiscale Framework for Spatial Modeling in Geography

规模依赖性是地理现象的固有属性，并且在最近的一些公共论坛中强调了更好地理解规模效应的日益紧迫的重要性。所谓的多尺度模型特别适合于这项任务，即在不同的空间和/或时间分辨率尺度下，根据被研究对象的组成结构对其整体结构进行分解的数学/统计模型。在这个项目中，工作将侧重于开发和实施一个多尺度统计建模框架，该框架是最近由主要研究人员专门为地理数据结构介绍的。这些模型的基础框架是数据空间的一组分层定义的分区（或聚合）。尺度的影响是通过对数据可能性的基本分解（或因式分解）来捕获的，由这种层次结构引起，在所有可能的空间分辨率下，将其分解为局部信息的各个组成部分。将这些多尺度可能性与适当定义的贝叶斯先验概率结构相结合，可以得到一个强大的推理框架。该项目的具体目标有三个方面：(i)进一步发展和扩展原有的一般建模结构，以便（ii）使其适合地理分析中的两类特定问题，即遥感和人口普查地理学的问题，最后（iii）产生正式的统计推断工具，以描述规模效应在预测、分类、知识发现和决策等标准任务中的影响。总的来说，这项研究的目的是充分发展一个推论统计框架，以研究地理现象中的尺度效应，特别强调遥感和人口普查地理学的问题。因此，它有望在地理理论、知识发现和空间数据挖掘以及数据库泛化的理论和方法等领域产生影响。所产生的框架将具有足够的灵活性和计算效率，以便将其纳入地理信息系统，例如在环境、流行病学和农业应用方面产生的地理信息系统。

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.