Bayesian Statistical Inference

Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy

Published by Princeton University Press

Published in print January 2014 | ISBN: 9780691151687
Published online October 2017 | e-ISBN: 9781400848911
Bayesian Statistical Inference

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This chapter introduces the most important aspects of Bayesian statistical inference and techniques for performing such calculations in practice. It first reviews the basic steps in Bayesian inference in early sections of the chapter, and then illustrates them with several examples in sections that follow. Numerical techniques for solving complex problems are next discussed, and the final section provides a summary of pros and cons for classical and Bayesian method. It argues that most users of Bayesian estimation methods are likely to use a mix of Bayesian and frequentist tools. The reverse is also true—frequentist data analysts, even if they stay formally within the frequentist framework, are often influenced by “Bayesian thinking,” referring to “priors” and “posteriors.” The most advisable position is to know both paradigms well, in order to make informed judgments about which tools to apply in which situations.

Keywords: Bayesian statistical inference; Bayesian techniques; Bayesian priors; Bayesian parameter uncertainty quantification; Bayesian model selection; nonuniform prior

Chapter.  31264 words.  Illustrated.

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