Innovations in Statistical Methodology and Applications to Economics, Engineering, Health, and Medicine

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The new millennium has witnessed the Big Data and Multi-cloud era which poses new challenges and opens up new opportunities for the mathematical (including statistical, computational, and data) sciences and their interactions with engineering, economics, finance, health and medicine. A long-term objective of this project is to develop innovative statistical methodologies and combine them with technological advances for resolving fundamental problems in these fields. Results of the project will have importance and relevance in personalized medicine, health and recommender systems, optimal dose-finding designs, reproducibility of scientific results under complex experiments, and on the foundations of machine and deep learning.The project is broadly divided into four areas. The first is the theory on implementation of nonparametric contextual bandits, with novel applications to personalized medicine and health and recommender systems. The second is nature-inspired metaheuristic optimization in artificial (machine) intelligence, particularly the solution of the long-standing open problem concerning on-line optimization of the tuning parameters of the metaheuristic algorithm in complex high-dimensional settings. One of its applications is optimal design of dose-finding trials in master protocols, which are studied in the third area of the project. The third area covers valid and efficient post-selection multiple testing in biomedicine and information technology in the big data era, for which some machine learning/feature engineering/variable selection algorithm is typically used to extract features/variables for subsequent hypothesis generation and statistical testing. The project will address the reproducibility issues and “replication crisis” with this data-dependent choice of features and hypotheses for statistical inference data by resolving foundational issues concerning valid post-selection inference. It also covers precision-guided drug and vaccine development and master protocols for early-phase and confirmatory clinical trials. Also covered are innovative study designs and analyses of point-of-care trials and observational studies, and development of mobile health platforms and wearable devices to improve and facilitate evidence-based management of chronic diseases. The fourth area is the statistical foundation of deep learning and provides the mathematical theory of convolutional neural networks and gradient descent, and applications to medical imaging and neuroscience. It also develops a novel Markov chain Monte Carlo method and closely related efficient adaptive particle filters in nonlinear state space models that have far-ranging applications in engineering and economics. The broader impacts of the project includes (i) direct applications in engineering, finance, insurance, risk management and surveillance, and (ii) developing new advanced courses and revising the curriculum in financial and risk modeling, statistics and data science, and clinical trials and biostatistics, which could positively impact the training of graduate and undergraduate students.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.