Statistical Rethinking (2/e)

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...

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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.

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...

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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.

Preface to the Second Edition
Preface
Audience
Teaching strategy
How to use this book
Installing the rethinking R package
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Preface to the Second Edition
Preface
Audience
Teaching strategy
How to use this book
Installing the rethinking R package
Acknowledgments
Chapter 1. The Golem of Prague
Statistical golems
Statistical rethinking
Tools for golem engineering
Summary
Chapter 2. Small Worlds and Large Worlds
The garden of forking data
Building a model
Components of the model
Making the model go
Summary
Practice
Chapter 3. Sampling the Imaginary
Sampling from a grid-appromate posterior
Sampling to summarize
Sampling to simulate prediction
Summary
Practice
Chapter 4. Geocentric Models
Why normal distributions are normal
A language for describing models
Gaussian model of height
Linear prediction
Curves from lines
Summary
Practice
Chapter 5. The Many Variables & The Spurious Waffles
Spurious association
Masked relationship
Categorical variables
Summary
Practice
Chapter 6. The Haunted DAG & The Causal Terror
Multicollinearity
Post-treatment bias
Collider bias
Confronting confounding
Summary
Practice
Chapter 7. Ulysses’ Compass
The problem with parameters
Entropy and accuracy
Golem Taming: Regularization
Predicting predictive accuracy
Model comparison
Summary
Practice
Chapter 8. Conditional Manatees
Building an interaction
Symmetry of interactions
Continuous interactions
Summary
Practice
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
Summary
Practice
Chapter 10. Big Entropy and the Generalized Linear Model
Mamum entropy
Generalized linear models
Mamum entropy priors
Summary
Chapter 11. God Spiked the Integers
Binomial regression
Poisson regression
Multinomial and categorical models
Summary
Practice
Chapter 12. Monsters and Mixtures
Over-dispersed counts
Zero-inflated outcomes
Ordered categorical outcomes
Ordered categorical predictors
Summary
Practice
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
Summary
Practice
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
Summary
Practice
Chapter 15. Missing Data and Other Opportunities
Measurement error
Missing data
Categorical errors and discrete absences
Summary
Practice
Chapter 16. Generalized Linear Madness
Geometric people
Hidden minds and observed behavior
Ordinary differential nut cracking
Population dynamics
Summary
Practice
Chapter 17. Horoscopes
Endnotes
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