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，这为数学（包括统计，计算和数据）科学及其与工程，经济，金融，健康和医学的相互作用带来了新的挑战并开辟了新的机遇。该项目的一个长期目标是发展创新的统计方法，并将其与技术进步相结合，以解决这些领域的根本问题。该项目的结果将在个性化医疗、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再现性以及机器和深度学习的基础上具有重要性和相关性。该项目大致分为四个领域。第一个是关于实现非参数上下文强盗的理论，其在个性化医疗和健康以及推荐系统中具有新颖的应用。第二个是自然启发式优化人工（机器）智能，特别是解决长期存在的公开问题，在线优化的元启发式算法的调整参数在复杂的高维设置。其应用之一是主协议中剂量探索试验的最佳设计，这是该项目第三个领域的研究。第三个领域涵盖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检验，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，以用于后续的假设生成和统计检验。该项目将解决再现性问题和“复制危机”，通过解决有关有效的后选择推理的基础问题，这种数据依赖的特征选择和统计推断数据的假设。它还涵盖精确指导的药物和疫苗开发以及早期和确证性临床试验的主协议。还涵盖了创新的研究设计和护理点试验和观察性研究的分析，以及移动的健康平台和可穿戴设备的开发，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。它还发展了一种新的马尔可夫链蒙特卡罗方法和密切相关的有效的自适应粒子滤波器在非线性状态空间模型，在工程和经济中有广泛的应用。该项目的更广泛影响包括：（一）在工程、金融、保险、风险管理和监督方面的直接应用;（二）开发新的高级课程，修订金融和风险建模、统计和数据科学、临床试验和生物统计方面的课程，该奖项反映了NSF的法定使命，并被认为是值得的。通过使用基金会的知识价值和更广泛的影响审查标准进行评估来提供支持。

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.