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This book includes the lectures given during the third session of the School of Statistics for Astrophysics that took place at Autrans, near Grenoble, in France, in October 2017. The subject is Bayesian Methodology. The interest of this statistical approach in astrophysics probably comes from its necessity and its success in determining the cosmological parameters from observations, especially from the cosmic background luctuations. The cosmological community has thus been very active in this field for many years. But the Bayesian methodology, complementary to the more classical frequentist one, has many applications in physics in general due to its ability to incorporate a priori knowledge into inference, such as uncertainty brought by the observational processes. The Bayesian approach becomes more and more widespread in the astrophysical literature. This book contains statistics courses on basic to advanced methods with practical exercises using the R environment, by leading experts in their field. This covers the foundations of Bayesian inference, Markov chain Monte Carlo technique, model building, Approximate Bayesian Computation (ABC) and Bayesian nonparametric inference and clustering.

Bayesian statistical decision theory. --- Bayes' solution --- Bayesian analysis --- Statistical decision

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The Bayesian approach to statistics and decision analysis is establishing itself as a powerful and practical tool to support the non-statistical, but otherwise technical, modeler. Recent advances in computational techniques have made Bayesian methods both accessible and widely applicable. This collection provides an argument for the wide application of Bayesian methods and includes an extensive collection of examples, techniques, and advice.

Mathematical statistics --- Bayesian statistical decision theory. --- Bayesian statistical decision theory --- Bayes' solution --- Bayesian analysis --- Statistical decision

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Statistical theory is primarily a product of the twentieth century. The prevailing school of thought builds on the frequentist philosophy developed by R.A. Fisher, the eminent biological theorist and experimentalist. Fisher's philosophy has been so thoroughly embraced that it has been labeled the ""classical"" approach, even though the alternative Bayesian philosophy antedates it by more than a century. Frequentist thinking has prevailed over Bayesian primarily because of the practical difficulty of fitting all but the simplest Bayesian models. Wildlife statistics has been almost entirely cond

Bayesian statistical decision theory. --- Ecology --- Mathematical models. --- Bayes' solution --- Bayesian analysis --- Statistical decision

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Bayesian Belief Networks are a powerful tool for combining different knowledge sources with various degrees of uncertainty in a mathematically sound and computationally efficient way. A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data modeling. First, because the model encodes dependencies among all variables, it readily handles situations where some data entries are missing. Second, a Bayesian network can be used to learn causal relationships, and hence can be used to gain an understanding about a problem domain and to predict the consequences of intervention. Third, because the model has both causal and probabilistic semantics, it is an ideal representation for combining prior knowledge (which often comes in a causal form) and data. Fourth, Bayesian statistical methods in conjunction with Bayesian networks offer an efficient and principled approach to avoid the over fitting of data.

Bayesian statistical decision theory. --- Bayes' solution --- Bayesian analysis --- Statistical decision --- Probability & statistics

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"Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years--at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information, even breaking Germany's Enigma code during World War II, and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security. Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time"--

Bayesian statistical decision theory --- Bayes' solution --- Bayesian analysis --- Statistical decision --- History. --- Mathematical statistics --- Bayes, Thomas