星系团的物理模拟与天体物理学中的贝叶斯推断
Physical modelling of galaxy clusters and Bayesian inference in astrophysics
摘要：
我比较了从弧分钟Microkelvin成像仪（AMI）无线电干涉仪系统和普朗克卫星的数据获得的质量值。前者使用贝叶斯分析管道，根据其物理量参数化集群，并分别使用Navarro-Frenk-White（NFW）和广义NFW配置文件对集群的暗物质和重子成分进行建模。我还分析了模拟AMI数据与输入值的基础上PwS质量估计。然后，我比较了三个集群模型使用AMI数据的54集群样本。这两个观测模型只考虑了星系团的气体含量。为了比较物理模型和观测模型，我考虑了它们的后验参数估计，包括计算两个概率分布之间定义的度量。通过查看贝叶斯证据值来评估模型对聚类数据的拟合。改进的物理建模的星系团，然后考虑，无论是放松一些假设的物理模型，或通过引入一个新的配置文件的暗物质组成的集群。聚类分析工作的最后一部分侧重于贝叶斯分析，同时使用AMI和普朗克卫星数据的联合似然函数。最后，提出了一种基于嵌套抽样的贝叶斯推断算法。该算法被称为“几何嵌套采样器”，是Metropolis-Hastings嵌套采样器的一种改进，它利用参数集的几何解释来有效地从它们的域中采样。几何嵌套采样器进行了测试，在几个玩具模型，以及一个模型代表的引力波发射的二进制黑洞合并。
英文摘要：
I compare the mass values obtained with data taken from the Arcminute Microkelvin Imager (AMI) radio interferometer system and from the Planck satellite. The former of these uses a Bayesian analysis pipeline that parameterises a cluster in terms of its physical quantities, and models the dark matter \& baryonic components of a cluster using Navarro-Frenk-White (NFW) and generalised-NFW profiles respectively. I also analyse simulated AMI data with input values based on PwS mass estimates. I then compare three cluster models using AMI data for the 54 cluster sample. The two observational models considered only model the gas content of the cluster. To compare the physical and observational models I consider their posterior parameter estimates, including the calculation of a metric defined between two probability distributions. The models' fit to the cluster data is evaluated by looking at the Bayesian evidence values. Improvements to the physical modelling of galaxy clusters are then considered, either by relaxing some of the assumptions underlying the physical model, or by introducing a new profile for the dark matter component of clusters. The final part of the cluster analysis work focuses on Bayesian analysis using a joint likelihood function of data from both AMI and the Planck satellite simultaneously. Finally, a new Bayesian inference algorithm based on nested sampling is presented. The algorithm, named the "geometric nested sampler", is an adaption of the Metropolis-Hastings nested sampler and makes use of the geometrical interpretation of sets of parameters to sample from their domains efficiently. The geometric nested sampler is tested on several toy models as well as a model representing the emission of gravitational waves from binary black hole mergers.
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