CAREER: Statistical foundations of particle tracking and trajectory inference

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到具有复杂动力学的大量运动的“粒子”。要了解这些系统是如何工作的，就需要开发统计程序，以便根据有噪音的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的、实用的和可靠的方法，特别关注开发统计理论在宇宙学、细胞生物学和机器学习中的应用。这项研究还将包括一个大型扩展部分，基于拓宽本科生和研究生的研究机会。该建议的技术目标是开发计算高效的估计器，当粒子基于已知或未知的随机过程演化时，用于d维多粒子跟踪，开发基于观测轨迹的后验抽样的贝叶斯方法，并扩展这些方法，以获得在概率度量的Wasserstein空间中平滑路径的极小极大估计过程。这项研究还旨在为具有粒子增长和相互作用的更具挑战性的模型开发估计器。这一奖项反映了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。

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.