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

本研究计划旨在发展研究气候资料时空函数的新方法。许多这样的数据序列本质上是振荡的，但不是严格的周期性，所描述的现象在不同时间点和全球不同地区的强度各不相同。对这些不规则振荡模式的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上的食物、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和建立更准确的预测系统也至关重要。本项目研究这些振荡型与其他气候变量的相互依赖性。这些结果有望促进对气候模式评估、不确定性量化和热带气旋行为的认识。软件开发是该项目的核心组成部分，将使从事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而得到训练。在这些不规则，多尺度和多维时空过程建模的主要统计挑战将使用功能数据方法来解决。将开发计算技术和理论机制，以便在功能数据和涉及这些数据的非参数和半参数模型中同时进行模型选择和推理。将开发基于计算的程序，以测试功能时空数据模型的拟合优度，并验证关于空间或时间依赖模式性质的技术假设。基于贝叶斯和重采样的推理程序将被开发并用于多个数据集。

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.