Cosmological Applications of Extreme Value Statistics

极值统计(EVS)是一种可以用来量化极端事件罕见程度的工具。它已被广泛用于预测现实世界中的极端事件，例如极端洪水、药物的副作用和进化过程中的突变事件。在宇宙学和天体物理学中，可以使用EVS来模拟稀有物体的丰度，例如宇宙中最大质量的星系团、最大的宇宙空洞、最大质量的原始黑洞和极端自转的黑洞。考虑到最近发射的詹姆斯-韦伯太空望远镜(JWST)和欧几里德卫星等新一代实验，电动汽车是一个及时的研究领域。利用EVS，我们可以预测星系、黑洞和星系团等极端天体的性质和丰度。这个项目探索了EVS的两个主要公式，即广义极值(GeV)方法和峰值超过阈值(POT)方法。从一些潜在的概率密度函数(Pdf)或累积密度函数(Cdf)描述的数据开始，我们应用两种EVS方法之一。目前，该项目的重点是使用EVS来预测红移为10-15的最亮星系的光度(JWST已经观测到)。我们使用GeV方法来计算基于各种光度函数的星系的最亮等等。然后我们制作图表，显示在一定红移范围内的预测峰值星等。然后，我们可以将电动汽车的预测与真实数据进行比较。整个项目将包含这些宇宙学应用的多个项目。除了最明亮的星系外，其他可能的主题还包括：-极端自旋双星系统及其相关的引力波。-活动星系核的极大质量。该项目本质上是跨学科的，并增加了华威数学研究所内研究的多样性。这项工作涉及到数学、统计学、物理学和计算机的交叉。该项目的精神是应用数学技术对物理观测进行建模，这样就需要对广义相对论和理论宇宙学有很好的理解。极值统计和贝叶斯参数推断是关键，以及执行数据分析和统计模拟所需的Python的使用。Joseph Silk(巴黎天体物理研究所)和Teerparb Chantavat博士(泰国基础研究所)是当前项目的合作者，两人都是Siri崇奇南的长期合作者。这项工作还可能涉及与华威的其他数学和天体物理学工作人员的合作。

Extreme-value statistics (EVS) is a tool that can be used to quantify the rarity of extreme events. It has been widely used to predict real-world extreme events, for example extreme floods, side effects of drugs, and mutational events during evolution. In cosmology and astrophysics, it is possible to use EVS to model the abundances of rare objects, such as the most massive galaxy clusters in the Universe, the largest cosmic voids, the most massive primordial black holes, and black holes with extreme spin. EVS is a timely area of research given the new generation of experiments such as the recently launched James-Webb Space Telescope (JWST) and Euclid satellite. Using EVS, we can make predictions about the nature and abundances of extreme astrophysical objects such as galaxies, black holes and clusters.This project explores the two main formulations of EVS, namely the Generalised Extreme Value (GEV) approach, and the Peaks-Over Threshold (POT) approach. Starting with data described by some underlying probability density function (pdf) or the cumulative density function (cdf), we apply one of the two EVS methodologies. Both yield different measures of rare events.Currently, the project focuses on using EVS to predict the luminosity of the brightest galaxies at redshifts 10-15 (which have been observed by JWST). We use the GEV approach to calculate the brightest magnitude of galaxies based off various luminosity functions. We then produce graphs which show the predicted peak magnitude over a range of redshifts. We can then compare our EVS predictions to real data. The overall project will contain multiple projects of these cosmological applications. Other possible topics besides the most luminous galaxies include: -Extreme-spin binary systems and their associated gravitational waves. -Extreme mass of active galactic nuclei. The project is interdisciplinary in nature and adds to the diversity of research within Warwick's Mathematics institute. The work involves an intersection of mathematics, statistics, physics, and computing. The spirit of the project is to apply mathematical techniques to model physical observations, such that it requires a good understanding of general relativity and theoretical cosmology. Extreme-value statistics and Bayesian parameter inference are key, as well as the use of Python required to perform data analysis and statistical simulations.Prof. Joseph Silk (Institut d'Astrophysique de Paris) and Dr. Teeraparb Chantavat (Institute for Fundamental Study, Thailand) are collaborators on the current project, both of whom are long-term collaborators of Siri Chongchitnan. Work will also potentially involve collaboration with other maths and astrophysics staff at Warwick.