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

新千年见证了大数据和多云时代，这对数学(包括统计、计算和数据)科学及其与工程、经济、金融、卫生和医学的互动提出了新的挑战，打开了新的机遇。该项目的一个长期目标是开发创新的统计方法，并将其与技术进步结合起来，以解决这些领域的根本问题。该项目的结果将在个性化医学、健康和推荐系统、最佳剂量发现设计、复杂实验下科学结果的重复性以及机器和深度学习的基础上具有重要和相关的意义。该项目大致分为四个领域。第一个是关于非参数上下文强盗实现的理论，以及在个性化医疗和健康和推荐系统中的新应用。第二种是人工(机器)智能中受自然启发的元启发式优化，特别是解决了复杂高维环境下元启发式算法的参数在线优化这一长期悬而未决的问题。它的应用之一是在主方案中优化剂量发现试验的设计，该方案在该项目的第三个领域进行了研究。第三个领域涵盖了大数据时代生物医学和信息技术中有效和高效的选择后多重测试，为此，通常使用一些机器学习/特征工程/变量选择算法来提取特征/变量，用于后续的假设生成和统计检验。该项目将通过解决与选择后有效推理有关的基本问题，通过这种依赖数据的统计推断数据特征和假设的选择，解决可再现性问题和“复制危机”。它还包括精确制导的药物和疫苗开发，以及早期和验证性临床试验的主方案。还包括对护理点试验和观察性研究的创新研究设计和分析，以及开发移动健康平台和可穿戴设备，以改善和促进慢性病的循证管理。第四个领域是深度学习的统计学基础，提供卷积神经网络和梯度下降的数学理论，以及在医学成像和神经科学中的应用。提出了一种新的马尔可夫链蒙特卡罗方法和与之密切相关的高效自适应粒子滤波方法，该方法在工程和经济领域有着广泛的应用。该项目的广泛影响包括(I)在工程、金融、保险、风险管理和监督方面的直接应用，以及(Ii)开发新的高级课程并修订金融和风险建模、统计学和数据科学、临床试验和生物统计学的课程，这可能会对研究生和本科生的培养产生积极影响。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.