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
How to use this book
Installing the rethinking R package
Chapter 1. The Golem of Prague
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
Curves from lines
Chapter 5. The Many Variables & The Spurious Waffles
Chapter 6. The Haunted DAG & The Causal Terror
Chapter 7. Ulysses’ Compass
The problem with parameters
Entropy and accuracy
Golem Taming: Regularization
Predicting predictive accuracy
Chapter 8. Conditional Manatees
Building an interaction
Symmetry of interactions
Chapter 9. Markov Chain Monte Carlo
Good King Markov and His island kingdom
Hamiltonian Monte Carlo
Easy HMC: ulam
Care and feeding of your Markov chain
Chapter 10. Big Entropy and the Generalized Linear Model
Generalized linear models
Mamum entropy priors
Chapter 11. God Spiked the Integers
Multinomial and categorical models
Chapter 12. Monsters and Mixtures
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
Categorical errors and discrete absences
Chapter 16. Generalized Linear Madness
Hidden minds and observed behavior
Ordinary differential nut cracking
Chapter 17. Horoscopes
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