Statistical Rethinking : A Bayesian Course with Examples in R and STAN book cover
2nd Edition

Statistical Rethinking
A Bayesian Course with Examples in R and STAN

ISBN 9780367139919
Published March 16, 2020 by Chapman and Hall/CRC
612 Pages

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Book Description

Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds your knowledge of and confidence in making inferences from data. Reflecting the need for scripting in today's model-based statistics, the book pushes you to perform step-by-step calculations that are usually automated. This unique computational approach ensures that you understand enough of the details to make reasonable choices and interpretations in your own modeling work.

The text presents causal inference and generalized linear multilevel models from a simple Bayesian perspective that builds on information theory and maximum entropy. The core material ranges from the basics of regression to advanced multilevel models. It also presents measurement error, missing data, and Gaussian process models for spatial and phylogenetic confounding.

The second edition emphasizes the directed acyclic graph (DAG) approach to causal inference, integrating DAGs into many examples. The new edition also contains new material on the design of prior distributions, splines, ordered categorical predictors, social relations models, cross-validation, importance sampling, instrumental variables, and Hamiltonian Monte Carlo. It ends with an entirely new chapter that goes beyond generalized linear modeling, showing how domain-specific scientific models can be built into statistical analyses.


  • Integrates working code into the main text
  • Illustrates concepts through worked data analysis examples
  • Emphasizes understanding assumptions and how assumptions are reflected in code
  • Offers more detailed explanations of the mathematics in optional sections
  • Presents examples of using the dagitty R package to analyze causal graphs
  • Provides the rethinking R package on the author's website and on GitHub

Table of Contents

 Preface to the Second Edition
 Teaching strategy
 How to use this book
 Installing the rethinking R package

 Chapter 1. The Golem of Prague
 Statistical golems
 Statistical rethinking
 Tools for golem engineering

 Chapter 2. Small Worlds and Large Worlds
 The garden of forking data
 Building a model
 Components of the model
 Making the model go

 Chapter 3. Sampling the Imaginary
 Sampling from a grid-appromate posterior
 Sampling to summarize
 Sampling to simulate prediction

 Chapter 4. Geocentric Models
 Why normal distributions are normal
 A language for describing models
 Gaussian model of height
 Linear prediction
 Curves from lines

 Chapter 5. The Many Variables & The Spurious Waffles
 Spurious association
 Masked relationship
 Categorical variables

 Chapter 6. The Haunted DAG & The Causal Terror
 Post-treatment bias
 Collider bias
 Confronting confounding

 Chapter 7. Ulysses’ Compass
 The problem with parameters
 Entropy and accuracy
 Golem Taming: Regularization
 Predicting predictive accuracy
 Model comparison

 Chapter 8. Conditional Manatees
 Building an interaction
 Symmetry of interactions
 Continuous interactions

 Chapter 9. Markov Chain Monte Carlo
 Good King Markov and His island kingdom
 Metropolis Algorithms
 Hamiltonian Monte Carlo
 Easy HMC: ulam
 Care and feeding of your Markov chain

 Chapter 10. Big Entropy and the Generalized Linear Model
 Mamum entropy
 Generalized linear models
 Mamum entropy priors

 Chapter 11. God Spiked the Integers
 Binomial regression
 Poisson regression
 Multinomial and categorical models

 Chapter 12. Monsters and Mixtures
 Over-dispersed counts
 Zero-inflated outcomes
 Ordered categorical outcomes
 Ordered categorical predictors

 Chapter 13. Models With Memory
 Example: Multilevel tadpoles
 Varying effects and the underfitting/overfitting trade-off
 More than one type of cluster
 Divergent transitions and non-centered priors
 Multilevel posterior predictions

 Chapter 14. Adventures in Covariance
 Varying slopes by construction
 Advanced varying slopes
 Instruments and causal designs
 Social relations as correlated varying effects
 Continuous categories and the Gaussian process

 Chapter 15. Missing Data and Other Opportunities
 Measurement error
 Missing data
 Categorical errors and discrete absences

 Chapter 16. Generalized Linear Madness
 Geometric people
 Hidden minds and observed behavior
 Ordinary differential nut cracking
 Population dynamics

 Chapter 17. Horoscopes


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Richard McElreath studies human evolutionary ecology and is a Director at the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany. He has published extensively on the mathematical theory and statistical analysis of social behavior, including his first book (with Robert Boyd), Mathematical Models of Social Evolution.


"The first edition (and this second edition) of *Statistical Rethinking* beautifully outlines the key steps in the statistical analysis cycle, starting from formulating the research question. I find that many statistics textbooks omit the issue of problem formulation and either jump into data acquisition or further into analysis after the fact. McElreath has created a fantastic text for students of applied statistics to not only learn about the Bayesian paradigm, but also to gain a deep appreciation for the statistical thought process. I also found that many students appreciated McElreath’s engaging writing style and humor, and personally found the infusion of humor quite refreshing."
~Adam Loy, Carleton College

"(The chapter) ‘Generalized Linear Madness’ represents another great chapter of an even better edition of an already awesome textbook."
~Benjamin K. Goodrich, Columbia University

"(Chapter 16) is a worthy concluding chapter to a masterful book. Eminently readable and enjoyable. Brimful of small thought-provoking bits which may inspire deeper studies, but first and foremost a window on the trial and error process involved in building a statistical model or rather, indeed, any scientific theory."
~Josep Fortiana Gregori, University of Barcelona

"I do regard the manuscript as technically correct, clearly written, and at an appropriate level of difficulty. The technical approaches and the R codes of the book are perfect for our students. They can learn concepts of Bayesian models, data analysis, and model validation methods through using the R codes. The codes help students to have better understanding of the models and data analysis process."
~Nguyet Nguyen, Youngstown State University

"In conclusion, Statistical Rethinking frames usual methods and tools taught in graduate statistical courses into a different way to encourage the reader to understand the details and appreciate the underlying assumptions. The accompanying R package offers example codes for some interesting problems that are not available in standard library or other popular packages. This book can be used as a supplement to a graduate course or it can be used by practitioners wanting to brush up their knowledge with better understanding of statistical techniques."
~Abhirup Mallik in Technometrics, August 2021

"As a textbook it successfully brings the statistician’s toolbox to a wider audience with an accessible style and good humour. It should be recommended to statistics students, both old and new."
~ Nathan Green, Journal of the Royal Statistical Society, 2021