Chapman and Hall/CRC
469 pages | 113 B/W Illus.
Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work.
The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation.
By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling.
The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.
"… I am quite impressed by Statistical Rethinking … I like the highly personal style with clear attempts to make the concepts memorable for students by resorting to external concepts. … it introduces Bayesian thinking and critical modeling through specific problems and spelled out R codes, if not dedicated datasets. Statistical Rethinking manages this all-inclusive most nicely … an impressive book that I do not hesitate recommending for prospective data analysts and applied statisticians!"
—Christian Robert (Université Paris-Dauphine, PSL Research University, and University of Warwick) on his blog, April 2016
"Statistical Rethinking is a fun and inspiring look at the hows, whats, and whys of statistical modeling. This is a rare and valuable book that combines readable explanations, computer code, and active learning."
—Andrew Gelman, Columbia University
"This is an exceptional book. The author is very clear that this book has been written as a course . . . Strengths of the book include this clear conceptual exposition of statistical thinking as well as the focus on applying the material to real phenomena."
—Paul Hewson, Plymouth University, 2016
"The book contains a good selection of extension activities, which are labelled according to difficulty. There are occasional paragraphs labelled ‘rethinking’ or ‘overthinking’ that contain finer details. The presentation is replete with metaphors ranging from the ‘statistical Golems’ in Chapter 1 through ‘Monsters and Mixtures’ in Chapter 11 and ‘Adventures in Covariance’ in Chapter 13."
—Diego Andrés Pérez Ruiz, University of Manchester
The Golem of Prague
Three tools for golem engineering
Small Worlds and Large Worlds
The garden of forking data
Building a model
Components of the model
Making the model go
Sampling the Imaginary
Sampling from a grid-approximate posterior
Sampling to summarize
Sampling to simulate prediction
Why normal distributions are normal
A language for describing models
A Gaussian model of height
Adding a predictor
Multivariate Linear Models
When adding variables hurts
Ordinary least squares and lm
Overfitting, Regularization, and Information Criteria
The problem with parameters
Information theory and model performance
Using information criteria
Building an interaction
Symmetry of the linear interaction
Interactions in design formulas
Markov Chain Monte Carlo
Good King Markov and His island kingdom
Markov chain Monte Carlo
Easy HMC: map2stan
Care and feeding of your Markov chain
Big Entropy and the Generalized Linear Model
Generalized linear models
Maximum entropy priors
Counting and Classification
Other count regressions
Monsters and Mixtures
Ordered categorical outcomes
Example: Multilevel tadpoles
Varying effects and the underfitting/overfitting trade-off
More than one type of cluster
Multilevel posterior predictions
Adventures in Covariance
Varying slopes by construction
Example: Admission decisions and gender
Example: Cross-classified chimpanzees with varying slopes
Continuous categories and the Gaussian process
Missing Data and Other Opportunities