Statistical Rethinking A Bayesian Course with Examples in R and STAN

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

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

Richard McElreath studies human evolutionary ecology and is a Director at the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany. He has published extensively on the mathematical theory and statistical analysis of social behavior, including his first book (with Robert Boyd), Mathematical Models of Social Evolution.