New Challenges, Models and Methods for Functional Data Analysis

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My research program will develop novel statistical methodologies by addressing applications in various disciplines such as genetics and public health. ******Our first research theme is functional data analysis (FDA), a growing area for analyzing curves, images, or any multidimensional functions. Common sources of functional data include fitness data from wearable devices, air pollution-related data, longitudinal studies, time-course gene expression data, and brain imaging data. The main challenge is dealing with the increasing scale and dimension of functional data while maintaining a balance between the flexibility and interpretability of FDA models. ******We will develop general and efficient FDA methods for high-dimensional functional/scalar variables. This research program will provide the foundation for various large-scale FDA models and have a broad impact in big data analysis. For instance, we will develop air pollution indices for various health outcomes. We will also study the correlation of brain signals among different brain locations. ******Our second research theme focuses on statistical inference for dynamical models. Dynamical models describe the rate of change of a dynamical system by using differential equations (DEs). They are widely used to understand complex systems in areas including biology and physics. While the parameters of DE models usually have scientific interpretations, their values are often unknown and are difficult to estimate. ******We will develop efficient methods that provide accurate and robust parameter estimates for DE models from real data and to link these DE parameters to high-dimensional functional and scalar predictors. This research program will fill the gap between DE modeling and real data analysis and make DE models popular and realistic in practical applications. For example, I propose to model the dynamical mechanism of large-scale networks, which provides not only the connection structure but also the regulation mechanism of networks. The proposed method can be applied to construct time-varying directed neural networks and social networks. I also propose to use partial differential equations to extract information from the seismogram data. This method will use seismogram data to produce high-definition images of subsurface geologic structures. This technology will be extremely useful for Canada's oil industry.******Not only will the proposed research support the training of highly qualified personnel, but it will also result in user-friendly software that we develop as solutions to the research problems tackled. This software will be available to the general public; we anticipate that its use by others will have a broad impact in research and industry. Furthermore, the proposed research is likely to impact the field of statistics through enabling groundbreaking advances in functional data analysis and statistical inference for dynamical models.**************