Bayesian models for astrophysical data. Using R, JAGS, Python, and Stan.

*(English)*Zbl 1366.62009
Cambridge: Cambridge University Press (ISBN 978-1-107-13308-2/hbk; 978-1-316-45951-5/ebook). xvii, 393 p. (2017).

The ten chapters of this book are: 1. Astrostatistics, 2. Prerequisites, 3. Frequentist vs. Bayesian methods, 4. Normal linear models, 5.-7. Generalized linear models, 8. Hierarchical generalized linear mixed models, 9. Model selection, 10. Astronomical applications. At the end, notes to the future of astrostatistics, three appendices, reference and subject index are given.

Chapter 1 gives a little of history, it says e.g., that the first application of the least square regression was to astrometrical purposes. Chapter 2 deals with the used software Stan, JAGS, R, and Python. Chapter 3 concentrates on Bayesian methods, it mentions the frequentist methods only in bypassing. Chapter 4 presents standard knowledge on the Gaussian models, whereas the next three chapters cover several of its possible generalizations like lognormal, gamma, inverse Gaussian, beta, binomial and Poisson models. Chapter 8 tells how the software covered can be used to tackle these models. Chapter 9 deals e.g. with the Bayesian LASSO (least absolute shrinkage and selection operator), and chapter 10 covers the following topics: black hole mass, supernovae, binary motion, initial mass function and globular cluster population.

Publisher’s description: This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA.

The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.

Chapter 1 gives a little of history, it says e.g., that the first application of the least square regression was to astrometrical purposes. Chapter 2 deals with the used software Stan, JAGS, R, and Python. Chapter 3 concentrates on Bayesian methods, it mentions the frequentist methods only in bypassing. Chapter 4 presents standard knowledge on the Gaussian models, whereas the next three chapters cover several of its possible generalizations like lognormal, gamma, inverse Gaussian, beta, binomial and Poisson models. Chapter 8 tells how the software covered can be used to tackle these models. Chapter 9 deals e.g. with the Bayesian LASSO (least absolute shrinkage and selection operator), and chapter 10 covers the following topics: black hole mass, supernovae, binary motion, initial mass function and globular cluster population.

Publisher’s description: This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA.

The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.

Reviewer: Hans-Jürgen Schmidt (Potsdam)

##### MSC:

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62P35 | Applications of statistics to physics |

62F15 | Bayesian inference |

62J12 | Generalized linear models (logistic models) |

85A35 | Statistical astronomy |

62-04 | Software, source code, etc. for problems pertaining to statistics |

85-02 | Research exposition (monographs, survey articles) pertaining to astronomy and astrophysics |

83C57 | Black holes |