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.
Features
Integrates working code into the main text
Illustrates concepts through worked data analysis examples
Emphasizes understanding assumptions and how assumptions are reflected in code
Offers more detailed explanations of the mathematics in optional sections
Presents examples of using the dagitty R package to analyze causal graphs
Provides the rethinking R package on the author's website and on GitHub
Contents
Chapter 1. The Golem of Prague
Statistical golems
Statistical rethinking
Tools for golem engineering
Chapter 2. Small Worlds and Large Worlds
The garden of forking data
Building a model
Components of the model
Making the model go
Chapter 3. Sampling the Imaginary
Sampling from a grid-approximate posterior
Sampling to summarize
Sampling to simulate prediction
Chapter 4. Geocentric Models
Why normal distributions are normal
A language for describing models
Gaussian model of height
Linear prediction
Curves from lines
Chapter 5. The Many Variables & The Spurious Waffles
Spurious association
Masked relationship
Categorical variables
Chapter 6. The Haunted DAG & The Causal Terror
Multicollinearity
Post-treatment bias
Collider bias
Confronting confounding
Chapter 7. Ulysses’ Compass
The problem with parameters
Entropy and accuracy
Golem Taming: Regularization
Predicting predictive accuracy
Model comparison
Chapter 8. Conditional Manatees
Building an interaction
Symmetry of interactions
Continuous interactions
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
Chapter 10. Big Entropy and the Generalized Linear Model
Maximum entropy
Generalized linear models
Maximum entropy priors
Chapter 11. God Spiked the Integers
Binomial regression
Poisson regression
Multinomial and categorical models
Chapter 12. Monsters and Mixtures
Over-dispersed counts
Zero-inflated outcomes
Ordered categorical outcomes
Ordered categorical predictors
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
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
Chapter 15. Missing Data and Other Opportunities
Measurement error
Missing data
Categorical errors and discrete absences
Chapter 16. Generalized Linear Madness
Geometric people
Hidden minds and observed behavior
Ordinary differential nut cracking
Population dynamics
Chapter 17. Horoscopes
Endnotes