Title: Bayesian Methods in Cosmology,
Abstract: These notes aim at presenting an overview of Bayesian statistics, the
underlying concepts and application methodology that will be useful to
astronomers seeking to analyse and interpret a wide variety of data about the
Universe. The level starts from elementary notions, without assuming any
previous knowledge of statistical methods, and then progresses to more
advanced, research-level topics. After an introduction to the importance of
statistical inference for the physical sciences, elementary notions of
probability theory and inference are introduced and explained. Bayesian methods
are then presented, starting from the meaning of Bayes Theorem and its use as
inferential engine, including a discussion on priors and posterior
distributions. Numerical methods for generating samples from arbitrary
posteriors (including Markov Chain Monte Carlo and Nested Sampling) are then
covered. The last section deals with the topic of Bayesian model selection and
how it is used to assess the performance of models, and contrasts it with the
classical p-value approach. A series of exercises of various levels of
difficulty are designed to further the understanding of the theoretical
material, including fully worked out solutions for most of them.