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.
Author(s): Richard McElreath
Preface
Audience
Teaching strategy
How to use this book
Installing the rethinking R package
Acknowledgments
1: The Golem of Prague
1.1. Statistical golems
1.2. Statistical rethinking
1.3. Three tools for golem engineering
1.4. Summary
2: Small Worlds and Large Worlds
2.1. The garden of forking data
2.2. Building a model
2.3. Components of the model
2.4. Making the model go
2.5. Summary
2.6. Practice
3: Sampling the Imaginary
3.1. Sampling from a grid-approximate posterior
3.2. Sampling to summarize
3.3. Sampling to simulate prediction
3.4. Summary
3.5. Practice
4: Linear Models
4.1. Why normal distributions are normal
4.2. A language for describing models
4.3. A Gaussian model of height
4.4. Adding a predictor
4.5. Polynomial regression
4.6. Summary
4.7. Practice
5: Multivariate Linear Models
5.1. Spurious association
5.2. Masked relationship
5.3. When adding variables hurts
5.4. Categorical variables
5.5. Ordinary least squares and lm
5.6. Summary
5.7. Practice
6: Overfitting, Regularization, and Information Criteria
6.1. The problem with parameters
6.2. Information theory and model performance
6.3. Regularization
6.4. Information criteria
6.5. Using information criteria
6.6. Summary
6.7. Practice
7: Interactions
7.1. Building an interaction
7.2. Symmetry of the linear interaction
7.3. Continuous interactions
7.4. Interactions in design formulas
7.5. Summary
7.6. Practice
8: Markov Chain Monte Carlo
8.1. Good King Markov and His island kingdom
8.2. Markov chain Monte Carlo
8.3. Easy HMC: map2stan
8.4. Care and feeding of your Markov chain
8.5. Summary
8.6. Practice
9: Big Entropy and the Generalized Linear Model
9.1. Maximum entropy
9.2. Generalized linear models
9.3. Maximum entropy priors
9.4. Summary
10: Counting and Classification
10.1. Binomial regression
10.2. Poisson regression
10.3. Other count regressions
10.4. Summary
10.5. Practice
11: Monsters and Mixtures
11.1. Ordered categorical outcomes
11.2. Zero-inflated outcomes
11.3. Over-dispersed outcomes
11.4. Summary
11.5. Practice
12: Multilevel Models
12.1. Example: Multilevel tadpoles
12.2. Varying effects and the underfitting/overfitting trade-off
12.3. More than one type of cluster
12.4. Multilevel posterior predictions
12.5. Summary
12.6. Practice
13: Adventures in Covariance
13.1. Varying slopes by construction
13.2. Example: Admission decisions and gender
13.3. Example: Cross-classified chimpanzees with varying slopes
13.4. Continuous categories and the Gaussian process
13.5. Summary
13.6. Practice
14: Missing Data and Other Opportunities
14.1. Measurement error
14.2. Missing data
14.3. Summary
14.4. Practice
15: Horoscopes
Endnotes
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Bibliography
Citation index
Topic index
