## A Bayesian Course with Examples in R and Stan (& PyMC3 & brms & Julia too, see links below)

**Most recent set of free lectures**: Statistical Rethinking 2023

### Second Edition

The second edition is now out in print. Publisher information on the CRC Press page. For more detail about what is new, look here.

### Materials

**2nd Edition**

- Book: CRC Press
- Book sample: Chapters 1 and 2 (2MB PDF)
- Lectures and slides:

* Winter 2024 (ongoing) - Code and examples:

* R package: rethinking (github repository)

* R code examples from the book: code.txt

* Book examples in Stan+tidyverse

* brms + tidyverse conversion here

* PyMC3 code examples: PyMC repository

* NumPyro!

* More NumPyro

* TensorFlow Probability notebooks

* Julia & Turing examples (both 1st and 2nd edition)

* Another Julia code translation with clean outline in notebook format

* R-INLA examples

* pyro/pytorch notebooks

* a new PyMC translation for the 3rd edition draft examples

* New PyMC5 translation for 2023 lecture examples

**1st Edition**

- Code and examples:

* R package: rethinking (github repository)

* Code examples from the book in plain text: code.txt

* 1st edition examples translated to brms syntax: Statistical Rethinking with brms, ggplot2, and the tidyverse

* 1st edition translated to Python & PyMC3

* 1st edition translated to Julia

* 1st edition examples as raw Stan - 1st edition errata: [view on github]

### Overview

**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.

### R package

The book is accompanied by an R package, `rethinking`. The package is available here and from on github. The core of this package is two functions, `quap` and `ulam`, that allow many different statistical models to be built up from standard model formulas. This has the virtue of forcing the user to lay out all of the assumptions. The function `quap` performs *maximum a posteriori* fitting. The function `ulam` builds a Stan model that can be used to fit the model using MCMC sampling. Some of the more advanced models in the last chapter are written directly in Stan code, in order to provide a bridge to a more general tool. There is also a technical manual with additional documentation.

### 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**