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Statistical Rethinking

Book Description

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.

Web Resource
The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.

Table of Contents

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