Data Fusion Approaches for Analysing Many Spatial Outcomes Jointly - Semiparametric Mixture Methods for Correlated Counting Processes and Joint Outcome Analyses

这项工作开发了新的统计工具，以解决数据分析中的严重问题，并将这些工具用于与水、监测和林业有关的重要应用。利用相关来源建立信息的统计方法是推动科学进步的关键需求；事实上，这一差距是环境计量学的一个主要障碍。如下所述，这项提案的重点是在几个相关项目中弥补这一差距。拟议的工具将用于联合绘制几种疾病或死亡率的地图，以确定地图上空间结构的共同点。可视化的比率很重要，因为这可能提供线索，提示可能与死亡或疾病有关的因素，以便进行进一步的详细研究。此外，地图提供了死亡率或发病率的总体描述，可以确定疾病不平等或对疾病具有抵抗力的领域。所开发的方法的优势在于它们能够考虑到数据的空间方面，以及因空间构型而存在的任何联系。通过这样做，这些方法能够为任何特定地区建立更好的估计，因为它们酌情在组合分析中使用地图中和跨地图的所有信息。更重要的是，地图上的空间连接本身就是人们感兴趣的，以便了解疾病的过程。我们将提出新的方法来分析自然过程，这些过程导致数据有许多零值，这在生态学研究中很常见。这项研究填补了处理这类不同数据的分析方法的空白。它将有助于处理在零之间和非零计数之间以及在这两个数据分类之间存在空间联系的情况，这种空间联系随着时间的推移而变化。在某些情况下，数据既包含大量的零，也包含大量的极值，例如在研究发生洪水的间歇性溪流中的河流流量时。长期以来，处理数据两端的极端情况的难度一直令水文学家感到沮丧。将利用新的统计工具来帮助建立以水文原理为基础的模型，以解决这些挑战。重要的是，这项研究考虑了从卫星图像中自动分离特定类型信息的工具的开发。这将提高对地监视的效率和效果。将开发新的方法来模拟混合空间数据源，如来自卫星数据和地面观测的数据，并改进利用卫星图像对森林火灾的监测。我们还将研究从卫星数据中提取信息的新方法，以估计农业用途的土壤水分。拟议的研究将有助于增加加拿大在这种复杂数据分析方面的专业知识。受训的学生将获得丰富的经验，增加新方法的开发，以及他们的知识和技能在学术界、工业界和政府机构中的适销性。

This work develops new statistical tools to address serious issues in data analysis and brings these to bear in important applications related to water, surveillance and forestry. Statistical methods for using related sources to build information are in critical demand for advancing science; indeed this gap is a major obstacle in environmetrics. The focus of this proposal is to address this gap in several related projects as described below. The proposed tools will serve to jointly map several diseases or mortality rates in order to identify the commonalities in the spatial structure across the maps. Visualizing rates is important because this may provide cues to suggest factors which may be linked to mortality or disease, for further detailed study. As well, maps provide an overall description of mortality or disease rates that can identify disease inequities or areas of resistance to disease. The strength of the methods developed is their capacity to take into account spatial aspects of the data, and any connections which exist because of spatial configurations. By so doing, the methods are able to build better estimates for any specific region, because they use all the information in the map, and across maps, in a combined analysis, as appropriate. More importantly, the spatial connections across the map are themselves of interest in order to understand the disease process. We will propose new ways for analyzing natural processes which result in data that have many zero values, which is common in ecological studies. This research fills the gap in analytical methods for handling this sort of disparate data. It will help to address situations where there is a spatial connection between the zeros and between the non-zero counts, as well as across these two compartments of the data, with this spatial connection changing over time. In some contexts, the data contain both an abundance of zeros and high extreme values, such as in studies of river flow in intermittent streams, where floods occur. The difficulty of dealing with extremes in both ends of the data has long frustrated hydrologists. New statistical tools will be brought to bear to aid in models which are based on hydrological principles to solve these challenges. Importantly, the research considers the development of tools to automatically isolate specific kinds of information from satellite images. This will raise the efficiency and effectiveness of earth surveillance. New methods will be developed to model mixed spatial data sources, such as from satellite data and ground observations, and improve surveillance of forest fires using satellite images. We will also study novel ways of extracting information from satellite data to estimate soil moisture for agricultural purposes. The proposed research will serve to increase expertise in Canada in such complex data analysis. Students trained will gain significant experience, increase development of new methods as well as the marketability of their knowledge and skill sets within academia, industry and at government agencies.