Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in the number of papers that employ Monte Carlo based Bayesian analysis. New, efficient Monte Carlo based methods are continuously being developed and explored. In this review, we first explain the basics of Bayesian theory and discuss how to set up data analysis problems within this framework. Next, we provide an overview of various Monte Carlo based methods for performing Bayesian data analysis. Finally, we discuss advanced ideas that enable us to tackle complex problems and thus hold great promise for the future. We also distribute downloadable computer software (available at this https URL ) that implements some of the algorithms and examples discussed here.

中文翻译：

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用于天文学贝叶斯数据分析的马尔可夫链蒙特卡罗方法

基于马尔可夫链蒙特卡罗的贝叶斯数据分析现在已成为几乎所有科学学科中分析和解释数据的首选方法。在天文学领域，在过去十年中，我们也看到采用基于蒙特卡罗贝叶斯分析的论文数量稳步增加。正在不断开发和探索新的、高效的基于蒙特卡罗的方法。在这篇综述中，我们首先解释了贝叶斯理论的基础知识，并讨论了如何在这个框架内设置数据分析问题。接下来，我们概述了用于执行贝叶斯数据分析的各种基于蒙特卡罗的方法。最后，我们讨论了先进的想法，使我们能够解决复杂的问题，从而对未来充满希望。