On Conditional Statistical Procedures for Simultaneous Model Selection, Inference, and Prediction in Complex Climate Systems

该研究项目旨在开发研究气候数据随时间和空间变化的新方法。许多这类数据系列具有振荡性质，但并非严格的周期性，所述现象在不同时间点和地球仪不同地区的强度各不相同。对这些不规则的振荡模式进行深入研究，对于规划基础设施需求、规划可持续发展以及管理地球的食物、水和能源资源至关重要。 了解气候数据对于解决人类，生态和环境问题的决策，更好地了解气候系统的物理过程以及更准确的预测系统也至关重要。该项目研究这些振荡模式和其他气候变量之间的相互依赖关系。预计这些结果将促进气候模式评估、不确定性量化和热带气旋行为方面的知识。软件开发是该项目的核心组成部分，将使研究相关数据分析问题的研究人员受益。 学生将通过参与跨学科的研究项目进行培训。将使用函数数据方法解决这些不规则，多尺度和多维时空过程建模的主要统计挑战。将开发计算技术和理论机器，用于在功能数据和涉及此类数据的非参数和半参数模型中同时进行模型选择和推断。将开发基于计算的程序，以测试功能时空数据模型的拟合度，并验证关于空间或时间依赖模式性质的技术假设。将开发贝叶斯和基于重新采样的推理程序并用于多个数据集。

This research project aims to develop new methodology for studying climate data as functions of time and space. Many such data series are oscillatory in nature but not strictly periodic, and the phenomena described vary in intensity at different points in time and in different parts of the globe. A thorough study of these irregular oscillatory patterns is of primary importance for planning of infrastructural needs, planning of sustainable development, and management of the planet's food, water, and energy resources. Understanding of climate data is also essential for decision-making to address human, ecological, and environmental concerns, for better understanding of the physical process of climate systems, and for more accurate predictive systems. This project studies the mutual dependence of these oscillatory patterns and other climate variables. The results are expected to advance knowledge in evaluation of climate models, uncertainty quantification, and tropical cyclone behavior. Software development, a core component of this project, will benefit researchers working on related data analytic problems. Students will be trained through involvement in the interdisciplinary research project.The primary statistical challenges in modeling these irregular, multi-scale and multi-dimensional spatio-temporal processes will be addressed using a functional data approach. Computational techniques and theoretical machinery will be developed for simultaneous model selection and inference in functional data and in non-parametric and semi-parametric models involving such data. Computation-based procedures will be developed for testing goodness of fit of models for functional spatio-temporal data and for verifying technical assumptions about the nature of spatial or temporal dependency patterns. Bayesian and resampling-based inferential procedures will be developed and used in multiple datasets.