Statistical Rethinking: A Bayesian Course with Examples in R and Stan
Abstract
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 ResourceThe 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.
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Prior predictive checks confirmed the appropriateness of the priors, and the training process converged with no diagnostic issues.
“Afterwards, we perform prior predictive checks to confirm their appropriateness [25]. Once assessing that the training process converged accordingly [37] and no diagnostic suggested issues [25], we evaluate the model.”
From Same Scrutiny, More Time: Eye Tracking Insights into Reviewing LLM-Labelled Code (2026) · cites this paper as [25]
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Makowski, D., Ben-Shachar, M., & Lüdecke, D. (2019) · Journal of Open Source Software · doi:10.21105/joss.01541 · Cited by 1,483 · see citing works
Indices of Effect Existence and Significance in the Bayesian Framework
Makowski, D., Ben-Shachar, M. S., Chen, S. H. A., & Lüdecke, D. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.02767 · Cited by 983 · see citing works
Matera, S., Schneider, W. F., Heyden, A., & Savara, A. (2019) · ACS Catalysis · doi:10.1021/acscatal.9b01234 · Cited by 222 · see citing works
A Bayesian Cognition Approach to Improve Data Visualization
Kim, Y.-S., Walls, L. A., Krafft, P., & Hullman, J. (2019) · Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems · doi:10.1145/3290605.3300912 · Cited by 76 · see citing works
Ross, C. T., Winterhalder, B., & McElreath, R. (2021) · Social Psychological and Personality Science · doi:10.1177/1948550620916071 · Cited by 61 · see citing works
Self-citationWartel, A., Lindenfors, P., & Lind, J. (2019) · PLOS ONE · doi:10.1371/journal.pone.0218655 · Cited by 40 · see citing works
Hatch, S. G., Knopp, K., Le, Y., Allen, M. O. T., Rothman, K., Rhoades, G. K., & Doss, B. D. (2022) · Family Process · doi:10.1111/famp.12710 · Cited by 28 · see citing works
Heteronormative relationship education for same-gender couples
Hatch, S. G., Rothman, K., Roddy, M. K., Dominguez, R. M., Le, Y., & Doss, B. D. (2021) · Family Process · doi:10.1111/famp.12548 · Cited by 23 · see citing works
Same Scrutiny, More Time: Eye Tracking Insights into Reviewing LLM-Labelled Code
Khojah, R., Gomes de Oliveira Neto, F., Mohamad, M., Frattini, J., & Leitner, P. (2026) · Proceedings of the 41st IEEE/ACM International Conference on Automated Software Engineering · doi:10.1145/3832783.3834423
- 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
- 2018-01-03
- OpenAlex
- W4247539597
- Cited by
- 726
- References
- 0
- Citations by year
- 2026: 109 · 2025: 165 · 2024: 111 · 2023: 67 · 2022: 73 · 2021: 70 · 2020: 72 · 2019: 37 · 2018: 11 · 2017: 7 · 2016: 1 · 2015: 2 · 2012: 1
- FWCI
- 11.84
- 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 › Statistics Education and Methodologies
- Keywords
- Bayesian analysis, statistical modeling, maximum entropy, measurement error, missing data, Gaussian processes, spatial autocorrelation, network autocorrelation, Stan, regression analysis
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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.
Statistics and arithmetic are recomputed, not judged.
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