Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In this paper, we review some fundamental concepts to understand Bayesian statistics and then introduce MCMC algorithms and samplers that allow us to perform the parameter inference procedure. We also introduce a general description of the standard cosmological model, known as the $\Lambda$CDM model, along with several alternatives, and current datasets coming from astrophysical and cosmological observations. Finally, with the tools acquired, we use an MCMC algorithm implemented in python to test several cosmological models and find out the combination of parameters that best describes the Universe.

中文翻译：

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使用贝叶斯统计进行宇宙学参数推断

贝叶斯统计和马尔可夫链蒙特卡罗 (MCMC) 算法已经在宇宙学领域找到了自己的位置。它们已成为重要的数学和数值工具，特别是在参数估计和模型比较方面。在本文中，我们回顾了一些基本概念来理解贝叶斯统计，然后介绍 MCMC 算法和采样器，使我们能够执行参数推理过程。我们还介绍了标准宇宙学模型的一般描述，称为$\Lambda$CDM 模型，以及几种替代方案，以及来自天体物理学和宇宙学观测的当前数据集。最后，利用获得的工具，我们使用在 Python 中实现的 MCMC 算法来测试几个宇宙学模型，并找出最能描述宇宙的参数组合。