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、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，以便根据噪声观测来估计这些动态。这项研究的目标是为这项任务开发可扩展、实用且可靠的方法，特别关注开发宇宙学、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基于扩大本科生和研究生研究机会的大型外展部分。该提案的技术目标是开发计算高效的估计器，用于当粒子基于已知或已知演化时在 d 维中进行多粒子跟踪。未知的随机过程，开发基于观察轨迹的后验采样贝叶斯方法，并扩展这些方法以获得概率测量的 Wasserstein 空间中平滑路径的极小极大估计程序。该研究还旨在开发估计器，用于更具挑战性的粒子生长和相互作用模型。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。