CAREER: Statistical foundations of particle tracking and trajectory inference

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具有复杂动力学的运动“粒子”的大量集合。要了解这些系统是如何工作的，就需要开发统计程序，在有噪声观测的基础上估计这些动态。本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，特别侧重于开发用于宇宙学、细胞生物学和机器学习的统计理论。这项研究还将包括一个基于扩大本科生和研究生获得研究机会的大型外展组成部分。本提案的技术目标是开发计算效率高的估计器，用于当粒子基于已知或未知的随机过程进化时在d维中跟踪多个粒子，开发基于观察轨迹的后验抽样贝叶斯方法，并扩展这些方法以获得概率测度的Wasserstein空间中光滑路径的极小极大估计程序。该研究还旨在开发更具挑战性的粒子生长和相互作用模型的估计器。该奖项反映了美国国家科学基金会的法定使命，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。

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.