Introduction to Bayesian Statistics with R

Author

Florian Hartig

Published

March 1, 2024

Preface

This course provides a practical introduction to Bayesian inference covering both the theory and application of Bayesian methods using a number of examples motivated from the biological and environmental sciences, including

  • Introduction to concepts of Bayesian statistics (Priors, Likelihoods, etc.)
  • Sampling methods (e.g. Markov Chain Monte Carlo) and model specification languages and frameworks (STAN, brms, BayesianTools)
  • Workflow of Bayesian inference, including model checks, model specification etc.
  • Bayesian model choice and model selection
  • Discussion of common hierarchical model structures, including mixed models, error in variable models, etc.

Organization of this book

This book is organized in three parts:

  1. Introduction and philosophy: The first part of this book provides a general introduction to Bayesian inference, starting with the internal logic (likelihood, prior, posterior), a short introduction on posterior estimation and interpretation, a section on Bayesian model selection and a overview of the Bayesian workflow
  2. Bayesian GLMMs: The second part covers how standard GLMMs (which could also be fit in R packages lme4 or glmmTMB) would be implemented in a Bayesian worklow
  3. Hierarchical models: The third part of the book shows examples of popular hierarchical model structures that may be the reason why you want to use Bayesian inference.

Assumed knowledge

This material assumes prior knowledge of standard statistical methods and concepts (tests, regressions, p-value, power, CIs, …) and the ability to apply those in R. At the University of Regensburg, this knowledge would be taught in the Bachelors Biology Lecture “Statistik und Bioinformatik” (lecture notes in German here), and the block course “Introduction to statistics in R”. If you didn’t take those or comparable courses, you should at least try to get some basic understanding of R before proceeding with this book. On top of that, a good grasp of GLMMs would be helpful for following this course. As a reference, have at my lecture notes on for the course Advanced Regression Models.

Acknowledgements

Much of this material was inspired by a serious of courses and summer schools that I did in various combinations of people, but mostly with my colleagues Jörn Page, Joe Chipperfield and Björn Reineking. Those past courses inlcuded

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