Practical Bayesian Inference: A Primer for Physical Scientists

Science is fundamentally about learning from data, and doing so in the presence of uncertainty. This volume is an introduction to the major concepts of probability and statistics, and the computational tools for analysing and interpreting data. It describes the Bayesian approach, and explains how this can be used to fit and compare models in a range of problems. Topics covered include regression, parameter estimation, model assessment, and Monte Carlo methods, as well as widely used classical methods such as regularization and hypothesis testing. The emphasis throughout is on the principles, the unifying probabilistic approach, and showing how the methods can be implemented in practice. R code (with explanations) is included and is available online, so readers can reproduce the plots and results for themselves. Aimed primarily at undergraduate and graduate students, these techniques can be applied to a wide range of data analysis problems beyond the scope of this work.

Table of Contents:
Preface; 1. Probability basics; 2. Estimation and uncertainty; 3. Statistical models and inference; 4. Linear models, least squares, and maximum likelihood; 5. Parameter estimation: single parameter; 6. Parameter estimation: multiple parameters; 7. Approximating distributions; 8. Monte Carlo methods for inference; 9. Parameter estimation: Markov chain Monte Carlo; 10. Frequentist hypothesis testing; 11. Model comparison; 12. Dealing with more complicated problems; References; Index.

About the Author :
Coryn A. L. Bailer-Jones was educated at the University of Oxford and the University of Cambridge. He has worked on modelling the processing of metals and has done research into the properties of low mass stars and brown dwarfs. He is a senior staff member at the Max-Planck-Institut für Astronomie, Heidelberg, where he leads a group working on the analysis of data from the Gaia survey mission. He also teaches statistics and physics at Universität Heidelberg. His main scientific interests are statistical inference, stars and our Galaxy, and the impact of astronomical phenomena on the Earth.

Review :
'Coryn Bailer-Jones provides a coherent introduction to the most important modern statistical methods and computational tools for analysing data. His writing style is easy to follow, without the burden of formal proofs and complex derivations, but with sufficient mathematical rigour. This book could be used as an excellent textbook for a semester-long course aimed at undergraduate and graduate students of physical sciences and engineering (knowledge of basic calculus is assumed, but no specific experience with probability or statistics is required). Theoretical concepts and examples of applications are extensively illustrated and supported by author's code in the R language.' Željko Ivezić, University of Washington 'Bailer-Jones' book is an excellent textbook that provides a simple yet rigorous introduction to statistical methods for data analysis. The book mainly focuses on Bayesian inference and parameter estimation and its goal is to make these topics accessible to a large variety of applied scientists interested in applying data analysis and uncertainty quantification to physical and natural science problems. … Overall, Bailer-Jones's book is an excellent resource for undergraduate students in STEM disciplines who wants to grasp an intuitive understanding of probability and statistics, and it is a comprehensive introductory handbook to keep on the bookshelf for graduate students and researchers in physical and natural sciences, interested in applying statistical methods for data analysis.' Dario Grana, Math Geosci 'Bailer-Jones does an excellent job of giving the reader an understanding of the techniques and the knowledge for further study in the subject … The care and effort that has been put into writing this book is clearly obvious. One of the author's intentions was, no doubt, to make the subject accessible and enjoyable and I think that goal has been achieved. Bailer-Jones has written an excellent book which uses real-life examples (in medicine and astronomy, for example) to explain the technique … I will make frequent use of this book for reference and will definitely give it a second reading.' Terence Morley, Mathematics Today 'The book can serve as a primer for undergraduate and graduate students or for researchers in physical and mathematical sciences whose interests lie in the application of statistical methods in analyzing complex data sets.' Fred Boadu, The Leading Edge 'Practical Bayesian Inference provides the fundamental concepts of probability and statistics as well as the computational mechanisms that an average student may use to extract maximum information from data plagued with uncertainties.' Fred Boadu, The Leading Edge