A Multiscale Framework for Spatial Modeling in Geography

规模依赖是地理现象的固有属性，最近的一些公共论坛强调了更好地了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，即数学/统计模型，在该模型中，研究对象的整体结构根据其在不同的空间和/或时间分辨率尺度上的成分结构被分解。在这个项目中，工作的重点将是开发和实施主要调查员最近专门针对地理数据结构推出的多尺度统计建模框架。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)来捕捉的，该数据可能性由该层次结构诱导成所有可能的空间分辨率的局部信息的单独分量。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，就会产生一个强大的推理框架。这个项目的具体目标有三个方面：(I)进一步发展和扩展原有的通用模型结构，以便(Ii)使其适用于地理分析中的两个特定类别的问题，即遥感和普查地理问题，以及(Iii)产生正式的统计推理工具，用于表征预测、分类、知识发现和决策等标准任务中的尺度效应的影响。因此，预计它将在地理理论、知识发现和空间数据挖掘以及数据库推广的理论和方法等领域产生影响。由此产生的框架将具有足够的灵活性和计算效率，以允许集成到地理信息系统(GIS)中，例如在环境、流行病学和农业应用的背景下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.