2nd Edition

Statistical Rethinking A Bayesian Course with Examples in R and STAN

By Richard McElreath Copyright 2020
    612 Pages
    by Chapman & Hall

    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

     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



    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