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Statistics, Data Mining, and Machine Learning in AstronomyA Practical Python Guide for the Analysis of Survey Data$
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Željko Ivezic, Andrew J. Connolly, Jacob T VanderPlas, and Alexander Gray

Print publication date: 2014

Print ISBN-13: 9780691151687

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691151687.001.0001

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Bayesian Statistical Inference

Bayesian Statistical Inference

Chapter:
(p.175) 5 Bayesian Statistical Inference
Source:
Statistics, Data Mining, and Machine Learning in Astronomy
Author(s):

Željko Ivezi

Andrew J. Connolly

Jacob T. VanderPlas

Alexander Gray

Željko Ivezi

Andrew J. Connolly

Jacob T. VanderPlas

Alexander Gray

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691151687.003.0005

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

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