Bayesian Methods in Cosmology

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Title: Bayesian Methods in Cosmology
Authors: Trotta, R
Item Type: Book
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.
Issue Date: 1-Jan-2009
URI: http://hdl.handle.net/10044/1/71193
Sponsor/Funder: Imperial College Trust
Engineering & Physical Science Research Council (E
European Commission
Science and Technology Facilities Council
Science and Technology Facilities Council (STFC)
Funder's Grant Number: NA
EP/K503733/1
H2020-MSCA-RISE-2015-691164
ST-N000838
ST/N000838/1
Keywords: astro-ph.CO
astro-ph.IM
stat.ME
Notes: 86 pages, 16 figures. Lecture notes for the 44th Saas Fee Advanced Course on Astronomy and Astrophysics, "Cosmology with wide-field surveys" (March 2014), to be published by Springer. Comments welcome
Appears in Collections:Physics
Astrophysics
Faculty of Natural Sciences



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