Statistical Rethinking

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.

The Golem of Prague
Statistical golems
Statistical rethinking
Three tools for golem engineering
Summary





Small Worlds and Large Worlds
The garden of forking data
Building a model
Components of the model
Making the model go
Summary
Practice





Sampling the Imaginary
Sampling from a grid-approximate posterior
Sampling to summarize
Sampling to simulate prediction
Summary
Practice





Linear Models
Why normal distributions are normal
A language for describing models
A Gaussian model of height
Adding a predictor
Polynomial regression
Summary
Practice





Multivariate Linear Models
Spurious association
Masked relationship
When adding variables hurts
Categorical variables
Ordinary least squares and lm
Summary
Practice





Overfitting, Regularization, and Information Criteria
The problem with parameters
Information theory and model performance
Regularization
Information criteria
Using information criteria
Summary
Practice





Interactions
Building an interaction
Symmetry of the linear interaction
Continuous interactions
Interactions in design formulas
Summary
Practice





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
Summary
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
Summary
Practice





Monsters and Mixtures
Ordered categorical outcomes
Zero-inflated outcomes
Over-dispersed outcomes
Summary
Practice





Multilevel Models
Example: Multilevel tadpoles
Varying effects and the underfitting/overfitting trade-off
More than one type of cluster
Multilevel posterior predictions
Summary
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
Summary
Practice





Missing Data and Other Opportunities
Measurement error
Missing data
Summary
Practice





Horoscopes