arXiv 0906.06642009-06astro-ph.COastro-ph.IM

宇宙学中的统计技术

Statistical techniques in cosmology

Alan Heavens

备注：: Typos corrected and exercises added

摘要：

在这些讲座中，我将涉及宇宙学数据分析的一些主题。我专注于宇宙学中常见的一般技术，或在宇宙学背景下发展起来的技术。事实上，对于在理论模型的背景下解释数据的问题，它们具有非常普遍的适用性，因此适合于贝叶斯处理。我们考虑从数据中估计参数的一般问题，并考虑如何使用Fisher矩阵来分析调查设计之前，采取任何数据，看看调查是否真的会做什么是必需的。我们概述了从数据中估计参数的数值方法，包括蒙特卡罗马尔可夫链和哈密顿蒙特卡罗方法。我们还研究了模型选择，它涵盖了各种场景，例如数据是否更喜欢一个额外的参数，或者回答更广泛的问题，例如哪种理论框架更受欢迎，使用广义相对论和膜世界引力作为例子。这些笔记不是文献综述，因此参考文献相对较少。

英文摘要：

In these lectures I cover a number of topics in cosmological data analysis. I concentrate on general techniques which are common in cosmology, or techniques which have been developed in a cosmological context. In fact they have very general applicability, for problems in which the data are interpreted in the context of a theoretical model, and thus lend themselves to a Bayesian treatment. We consider the general problem of estimating parameters from data, and consider how one can use Fisher matrices to analyse survey designs before any data are taken, to see whether the survey will actually do what is required. We outline numerical methods for estimating parameters from data, including Monte Carlo Markov Chains and the Hamiltonian Monte Carlo method. We also look at Model Selection, which covers various scenarios such as whether an extra parameter is preferred by the data, or answering wider questions such as which theoretical framework is favoured, using General Relativity and braneworld gravity as an example. These notes are not a literature review, so there are relatively few references.

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摘要：

英文摘要：

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