论文标题
重力波天文学中的模型探索,人口可能性最大
Model exploration in gravitational-wave astronomy with the maximum population likelihood
论文作者
论文摘要
分层贝叶斯推断是研究带有重力波的紧凑型二进制物的种群特性的重要工具。基本前提是推断二进制黑洞和/或中子星参数的未知先前分布,例如组分质量,自旋矢量和红移。这些分布揭示了巨大的恒星的命运,如何组装二进制物以及宇宙在宇宙时间上的演变。分层分析使用以数据为条件的先验分布来模拟二进制黑洞的模型,这是从数据中推断出来的。但是,误指定的模型可能导致天体物理的错误推断。在本文中,我们回答了一个问题:给定一些数据,这些数据是先前的分布 - 从所有可能的先前分布的集合中 - 产生了可能的人群可能性最大?此分布(不是真正的先验)是$ \ pistroke $(发音为“ Pi Stroke”),而关联的\ textit {最大群体可能性}为$ \ lstroke $(发音为“ l Stroke”)。 $ \ pistroke $的结构是Delta函数的线性叠加,结果是Carath {é} Odory的定理。我们展示了$ \ pistroke $和$ \ lstroke $如何用于模型探索/批评。我们将这种$ \ lstroke $形式主义应用于Ligo-Virgo中观察到的二进制黑洞合并的种群 - Kagra的第三个重力波瞬时目录。根据我们的结果,我们讨论了重力波种群模型的可能改进。
Hierarchical Bayesian inference is an essential tool for studying the population properties of compact binaries with gravitational waves. The basic premise is to infer the unknown prior distribution of binary black hole and/or neutron star parameters such component masses, spin vectors, and redshift. These distributions shed light on the fate of massive stars, how and where binaries are assembled, and the evolution of the Universe over cosmic time. Hierarchical analyses model the binary black hole population using a prior distribution conditioned on hyper-parameters, which are inferred from the data. However, a misspecified model can lead to faulty astrophysical inferences. In this paper we answer the question: given some data, which prior distribution--from the set of all possible prior distributions--produces the largest possible population likelihood? This distribution (which is not a true prior) is $\pistroke$ (pronounced "pi stroke"), and the associated \textit{maximum population likelihood} is $\Lstroke$ (pronounced "L stroke"). The structure of $\pistroke$ is a linear superposition of delta functions, a result which follows from Carath{é}odory's theorem. We show how $\pistroke$ and $\Lstroke$ can be used for model exploration/criticism. We apply this $\Lstroke$ formalism to study the population of binary black hole mergers observed in LIGO--Virgo--KAGRA's third Gravitational-Wave Transient Catalog. Based on our results, we discuss possible improvements for gravitational-wave population models.