CAREER: Statistical foundations of particle tracking and trajectory inference

职业：粒子跟踪和轨迹推断的统计基础

• 批准号: 2339829
• 负责人: Jonathan Niles-Weed
• 金额: $ 44.99万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-04-01 至 2029-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2339829&HistoricalAwards=false
• 关键词: CAREER; Statistical; foundations; particle; tracking

Many problems in human microbiology, astronomy, high-energy physics, fluid dynamics, and aeronautics involve large collections of moving "particles" with complicated dynamics. Learning how these systems work requires developing statistical procedures for estimating these dynamics on the basis of noisy observations. The goal of this research is to develop scalable, practical, and reliable methods for this task, with a particular focus on developing statistical theory for applications in cosmology, cellular biology, and machine learning. This research will also include a large outreach component based on broadening access to research opportunities for undergraduates and graduate students.The technical goals of this proposal are to develop computationally efficient estimators for multiple particle tracking in d dimensions when the particles evolve based on a known or unknown stochastic process, to develop Bayesian methods for posterior sampling based on observed trajectories, and to extend these methods to obtain minimax estimation procedures for smooth paths in the Wasserstein space of probability measures. The research also aims to develop estimators for more challenging models with the growth and interaction of particles.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.

人类微生物学、天文学、高能物理学、流体动力学和航空学中的许多问题都涉及大量具有复杂动力学的运动“粒子”。了解这些系统如何工作，需要开发统计程序，以估计这些动态的基础上嘈杂的意见。这项研究的目标是为这项任务开发可扩展的，实用的和可靠的方法，特别侧重于开发宇宙学，细胞生物学和机器学习应用的统计理论。这项研究还将包括一个大的外展组成部分的基础上扩大获得研究机会的本科生和研究生。该建议的技术目标是开发计算效率的估计多个粒子跟踪在d维时，粒子演变的基础上一个已知或未知的随机过程，发展贝叶斯方法后验抽样的基础上观察到的轨迹，并将这些方法推广到Wasserstein概率测度空间中光滑路径的极大极小估计。该研究还旨在为更具挑战性的粒子增长和相互作用模型开发估算器。该奖项反映了NSF的法定使命，并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，被认为值得支持。