Computationally Tractable Inference for Multi-Messenger Astrophysics

多信使天体物理学利用多种观测方式，如引力波、光、中微子和宇宙射线，来观测天体物理事件和物体。在多信使天体物理学中出现的两个具体问题激发了这个研究项目：探测引力波和电磁天空图之间的相互关系，以及约束中子星状态方程。用多信使观测产生的数据正式解决这些问题提出了挑战，需要开发新的统计和计算方法。本项目旨在发展改进的(1)统计技术，用于探测推测引力波背景与宇宙微波背景天图之间的相互关系；(2)贝叶斯算法，用于分析双中子星合并中的引力波特征。这项研究将为下一代统计学家和天文学家的专业发展提供跨学科的机会。该项目将侧重于开发对计算复杂性高的多维参数模型进行拟合优度检验的方法，特别注意查明建模错误的来源。另一个重点将是在低维（状态空间和观测数据的固定大小）和高维（观测数据和状态空间的大小同时增加）制度下开发马尔可夫链蒙特卡罗方法的收敛分析方法。这些制度的趋同分析应被视为互补的；如果没有这样的收敛性分析，从业者评估MCMC实验可靠性的能力就会受到限制，因此也就无法进行任何后续的推断。这些新方法将通过开源软件向公众开放。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。

Multi-messenger astrophysics leverages multiple modalities of observations, such as gravitational waves, light, neutrinos, and cosmic rays, to observe astrophysical events and objects. Two specific issues arising in multi-messenger astrophysics motivate much of this research project: detecting cross-correlation between gravitational waves and electromagnetic sky maps and constraining the neutron star equation of state. Addressing these issues formally with the data produced from multi-messenger observations presents challenges that require the development of novel statistical and computational methodology. This project aims to develop improved (1) statistical techniques for detecting cross-correlation between a conjectured gravitational wave background and the cosmic microwave background sky map and (2) Bayesian algorithms for analysis of gravitational wave signatures in binary neutron star mergers. The research will provide interdisciplinary opportunities for professional development of the next generation of statisticians and astronomers. The project will focus on developing methods for performing goodness-of-fit tests for multidimensional parametric models characterized by high computational complexity, paying particular attention to identifying the sources of mismodelling. Another focus will be developing methods for convergence analysis of Markov chain Monte Carlo methods in both low-dimensional (fixed sizes of state space and observed data) and in high-dimensional (size of observed data and state space increase simultaneously) regimes. Convergence analysis in these regimes should be viewed as complementary; without such convergence analyses, practitioners have limited ability to assess the reliability of their MCMC experiments and hence any subsequent inference. The new methods will be made publicly available through open-source software.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.