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。多信使天体物理学中出现的两个具体问题推动了这一研究项目的大部分：探测引力波和电磁天空图之间的相互关联，以及约束中子星的状态方程。用多信使观测产生的数据正式处理这些问题是一项挑战，需要开发新的统计和计算方法。该项目旨在开发改进的(1)用于检测推测的引力波背景与宇宙微波背景天空图之间的互相关的统计技术，以及(2)用于分析双星中子星合并中的引力波特征的贝叶斯算法。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具有高度计算复杂性的多维参数模型进行拟合优度测试的方法，并特别注意查明错误建模的来源。另一个重点将是发展马尔科夫链蒙特卡罗方法在低维(固定状态空间和观测数据的大小)和高维(观测数据和状态空间的大小同时增加)下的收敛分析方法。在这些制度下的收敛分析应被视为互补的；如果没有这种收敛分析，从业者评估其MCMC实验的可靠性的能力有限，因此任何后续推理都是有限的。新的方法将通过开源软件公开。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。

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.