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

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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.