Novel Statistical Methods with Applications to Massive and Complex Dynamic Data

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With the advent of modern technologies, massive and complex dynamic data have received increasing attention. Examples of massive and complex dynamic data include single-cell RNA sequencing data, functional magnetic resonance imaging data, and electronic health record data. Statistical analysis of these data, however, has been extremely difficult due to their sheer size and complexity. This proposal is devoted to developing a new set of statistically systematic and computationally efficient methods for analyzing massive and complex dynamic data. The proposed project has the following interrelated themes. First, the PI will model trajectories of different cell types using discrete entropy regularized optimal transport and develop a change point detection method to infer the time these cells differentiate. Second, the PI proposes to build time series models for brain dynamic functional connectivity and detect dynamic changes to help understand the relationship between brain subregions. Third, the PI plans to study weighted functional principal component analysis with informative observations. The methods will be applied to electronic health records for disease prediction and causal discovery. The statistical methods developed in this proposal are timely and important and will be relevant to many large-scale complex dynamic real data sets, for example, the Human Connectome Project and the UK Biobank. The proposed research promises to have a huge impact by contributing to groundbreaking advancements in genetics and genomics, neuroscience, and medical science. Undergraduate and graduate students will receive excellent training to help them to gain valuable skills that qualify them for attractive positions in universities, research hospitals, and industries. In order to facilitate the use of the proposed new methods, the PI will implement them in R or Python and make software available to the public, along with publishing the corresponding research reports.