The article "Bayes in the Sky: Bayesian Inference and Model Selection in Cosmology" by Roberto Trotta provides an introduction to Bayesian methods in cosmology and astrophysics. It highlights the growing importance of Bayesian methods due to the increasing size and complexity of data sets, which have made numerical inference feasible. The author discusses the conceptual underpinnings of Bayesian probability theory, including Bayes' Theorem and the role of priors. He also covers the application of Bayesian methods to numerical techniques like Monte Carlo Markov Chain (MCMC) methods for parameter inference and model comparison. The review emphasizes the advantages of Bayesian methods over traditional statistical tools, such as higher efficiency and a consistent conceptual basis for dealing with uncertainty. Recent developments in cosmological parameter extraction and Bayesian cosmological model building are discussed, along with the challenges that lie ahead. The article concludes by summarizing the key concepts and recent advancements in Bayesian methods in cosmology.The article "Bayes in the Sky: Bayesian Inference and Model Selection in Cosmology" by Roberto Trotta provides an introduction to Bayesian methods in cosmology and astrophysics. It highlights the growing importance of Bayesian methods due to the increasing size and complexity of data sets, which have made numerical inference feasible. The author discusses the conceptual underpinnings of Bayesian probability theory, including Bayes' Theorem and the role of priors. He also covers the application of Bayesian methods to numerical techniques like Monte Carlo Markov Chain (MCMC) methods for parameter inference and model comparison. The review emphasizes the advantages of Bayesian methods over traditional statistical tools, such as higher efficiency and a consistent conceptual basis for dealing with uncertainty. Recent developments in cosmological parameter extraction and Bayesian cosmological model building are discussed, along with the challenges that lie ahead. The article concludes by summarizing the key concepts and recent advancements in Bayesian methods in cosmology.