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Statistical Rethinking


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Table of Contents

The Golem of Prague
Statistical golems
Statistical rethinking
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
Practice Sampling the Imaginary
Sampling from a grid-approximate posterior
Sampling to summarize
Sampling to simulate prediction
Practice Linear Models
Why normal distributions are normal
A language for describing models
A Gaussian model of height
Adding a predictor
Polynomial regression
Practice Multivariate Linear Models
Spurious association
Masked relationship
When adding variables hurts
Categorical variables
Ordinary least squares and lm
Practice Overfitting, Regularization, and Information Criteria
The problem with parameters
Information theory and model performance
Information criteria
Using information criteria
Practice Interactions
Building an interaction
Symmetry of the linear interaction
Continuous interactions
Interactions in design formulas
PracticeMarkov Chain Monte Carlo
Good King Markov and His island kingdom
Markov chain Monte Carlo
Easy HMC: map2stan
Care and feeding of your Markov chain
Practice Big Entropy and the Generalized Linear Model
Maximum entropy
Generalized linear models
Maximum entropy priors
Summary Counting and Classification
Binomial regression
Poisson regression
Other count regressions
Practice Monsters and Mixtures
Ordered categorical outcomes
Zero-inflated outcomes
Over-dispersed outcomes
Practice Multilevel Models
Example: Multilevel tadpoles
Varying effects and the underfitting/overfitting trade-off
More than one type of cluster
Multilevel posterior predictions
Practice 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
Practice Missing Data and Other Opportunities
Measurement error
Missing data
Practice Horoscopes

About the Author

Richard McElreath is the director of the Department of Human Behavior, Ecology, and Culture at the Max Planck Institute for Evolutionary Anthropology. He is also a professor in the Department of Anthropology at the University of California, Davis. His work lies at the intersection of evolutionary and cultural anthropology, specifically how the evolution of fancy social learning in humans accounts for the unusual nature of human adaptation and extraordinary scale and variety of human societies.


"... 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 (Universite 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 Andres Perez Ruiz, University of Manchester

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