The textbook Statistical Rethinking: a Bayesian course with examples in R and Stan, by Richard McElreath, has been very well-received since the publication of its first edition in February 2016. The second edition was published relatively recently in March 2020. Statistical Rethinking is an attempt to bring the modern versions of what was started by statisticians, back with the likes of GLIM and BUGS, to a wider audience who do not necessarily have much prior knowledge in maths, stats and computing.

The book is about model building, what can go wrong and how to look out for it. Statistical concepts are presented with some great examples throughout the book, including using examples of geocentric models, waffle house locations in the United States, Ulysses’ Compass and horoscopes. Structurally, the book is roughly split into groups of chapters. In Chapter 1, the ideas of the Golem of Prague are introduced. This is used to explain how scientific models are constructed. They are without intent of their own, bumbling along and their use entails some risk. This is a key principle in the book and returned to often throughout. Chapters 2 and 3 cover the introduction of Bayesian ideas. Simulation is the preferred approach to help explain concepts, rather than relying on equations, and I think this works. Chapters 4 to 8 show how to build multiple linear models. They include sections on spurious association, masked relationships, directed acyclic graph (DAGS) and causal inference, multicollinearity, bias and confounding, regularization, predicting predictive accuracy, model comparison and interactions. Chapters 9 to 12 are about generalized linear models. This includes discussion of MCMC and maximum entropy. The types of models covered are binomial, Poisson and multinomial regression, and when we have overdispersed counts and zero-inflated outcomes. Chapters 13 to 16 are about multilevel models, measurement error and missing data. Finally, Chapter 17 is an entirely new chapter that goes beyond generalized linear modelling, showing how domain-specific scientific models can be built into statistical analyses. The second edition has made considerable changes to the first. It now emphasizes the DAG approach to causal inference. Other new additions include material on the design of prior distributions, splines, ordered categorical predictors, social relations models, cross-validation, importance sampling, instrumental variables and Hamiltonian Monte Carlo.

The book is aimed at a very broad readership. It contains very little formal mathematics. The book’s outline explicitly says that you do not require much coding experience or quantitative training. The author’s style has a friendly, conversational tone. The stories and analogies are welcome jumping-off points to more sophisticated ideas. Finally, the author does not take himself too seriously. The result of this approach seems to be to produce a non-threatening statistics textbook which still manages to have some substance behind it.

This is an excellent textbook, and any criticism is minor. I believe that this book will not teach you Stan or R. The code used in the book uses functions from the author’s own package rethinking so what you learn will be specific to this. That said, some of the more advanced models in the last chapter are written directly in Stan code, and there are plenty of other resources out there to learn R.

In conclusion, Statistical Rethinking will complement other more technical textbooks in statistics, R and Stan. 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.

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