Statistical Rethinking: A Bayesian Course with Examples in R and Stan
Abstract
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
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Pre-exposure vaccination intent was modelled as a monotonic ordered predictor to control for sampling discrepancies between the treatment and control groups and to allow the treatment to differentially affect those with different prior vaccination intents.
“W is modelled as a monotonic ordered predictor 63,64 . Using W as a predictor for Y has two advantages: it (1) controls for sampling discrepancies between the treatment and control groups, and (2) allows for the treatment to differentially affect those with different prior vaccination intents.”
From Measuring the impact of COVID-19 vaccine misinformation on vaccination intent in the UK and USA (2021) · cites this paper as [64]
Bayesian analysis remains robust even in the case of smaller sample sizes.
“We conducted a Bayesian analysis to gain a probabilistic understanding of the treatment effects, an approach that remains robust even in the case of smaller sample sizes (McElreath 2020).”
From Echoes of AI: Investigating the downstream effects of AI assistants on software maintainability (2026) · cites this paper as McElreath 2020
Bayesian methods yield more intuitive uncertainty metrics.
“(c) more intuitive uncertainty metrics”
From Effects of Availability, Contingency, and Formulaicity on the Accuracy of English Grammatical Morphemes in Second Language Writing (2022) · cites this paper as McElreath, 2020
Bayesian methods yield the full posterior distribution that is more informative than point estimates.
“(b) the full posterior distribution that is more informative than point estimates”
From Effects of Availability, Contingency, and Formulaicity on the Accuracy of English Grammatical Morphemes in Second Language Writing (2022) · cites this paper as McElreath, 2020
Bayesian methods yield more reliable parameter estimates in complex statistical models.
“More generally, in comparison to frequentist analyses, Bayesian methods yield (a) more reliable parameter estimates in complex statistical models such as the ones used in our study”
From Effects of Availability, Contingency, and Formulaicity on the Accuracy of English Grammatical Morphemes in Second Language Writing (2022) · cites this paper as McElreath, 2020
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- Authors
- McElreath, R.
- Affiliations
- Max Planck Institute for Evolutionary Anthropology (DE)
- Corresponding author
- McElreath, Richard
- ORCID
- McElreath, Richard
- Venue
- Chapman & Hall/CRC eBooks
- Publisher
- Chapman and Hall/CRC
- Published
- 2020-03-13
- OpenAlex
- W4232976691
- Cited by
- 1,959
- References
- 0
- Citations by year
- 2026: 297 · 2025: 385 · 2024: 325 · 2023: 317 · 2022: 268 · 2021: 223 · 2020: 96 · 2019: 36 · 2018: 6 · 2017: 2 · 2016: 3 · 2013: 1
- FWCI
- 101.46
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Chapman & Hall/CRC eBooks (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Data Analysis with R
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Keywords
- Bayesian inference, causal inference, directed acyclic graphs, maximum entropy, information theory, measurement error, missing data, Gaussian processes, spatial confounding, splines, social relations model, cross-validation, importance sampling, instrumental variables, Hamiltonian Monte Carlo, Stan, R
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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