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Bayesian Data Analysis
Abstract
Bayesian Data Analysis describes how to conceptualize, perform, and critique statistical analyses from a Bayesian perspective. Using examples largely from the authors' own experiences, the book focuses on modern computational tools and obtains inferences using computer simulations. Its unique features include thorough discussions of the methods for
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“The inverse-gamma(α, β) model for σ 2 α can also be expressed as an inverse-χ 2 distribution with scale s 2 α = β/α and degrees of freedom ν α = 2α (Gelman et al., 2003).”
From Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) (2006) · cites this paper as Gelman et al., 2003
In the citing paper
“With J = 1 or 2 groups, this actually results in an improper posterior density, essentially concluding σ α = ∞ and doing no shrinkage (see Gelman et al., 2003, Exercise 5.8).”
From Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) (2006) · cites this paper as Gelman et al., 2003, Exercise 5.8
In the citing paper
“Their capacity to handle uncertainty, incorporate prior knowledge, and update beliefs based on evidence makes them effective for modeling complex systems (Gelman et al. 1995; MacKay 2003).”
From The myth of the Bayesian brain (2025) · cites this paper as Gelman et al. 1995
In the citing paper
“We adopt Bayesian statistics for its advantages in being able to hypothesize null effects[27,73].”
From Explanations Can Reduce Overreliance on AI Systems During Decision-Making (2023) · cites this paper as [27]
In the citing paper
“To improve the efficiency of this procedure, I use a Hamiltonian Monte Carlo algorithm (Gelman et al. 2013) and employ a hierarchical setup that considers each of the four sets of parameters as draws from four common population distributions:”
From Birds of the Same Feather Tweet Together: Bayesian Ideal Point Estimation Using Twitter Data (2015) · cites this paper as Gelman et al. 2013
In the citing paper
“Because this model is a Bayesian extension of a conventional MFRM, its parameter estimates approach those of a non-Bayesian conventional MFRM when we have a large amount of data, which is a desirable property.”
From A Bayesian many-facet Rasch model with Markov modeling for rater severity drift (2022) · cites this paper as Gelman et al., 2013
In the citing paper
“The parameter estimates of a Bayesian model are known to approach those of its non-Bayesian counterpart as the amount of data increases. This is because the influence of the prior distribution decreases (Gelman et al., 2013).”
From A Bayesian many-facet Rasch model with Markov modeling for rater severity drift (2022) · cites this paper as Gelman et al., 2013
In the citing paper
“The use of model families is also accomodated naturally within the framework of hierarchical Bayesian models [1] and is proposed to address the well known issue of model dilution [4].”
From Comparing families of dynamic causal models (2010) · cites this paper as [1]
In the citing paper
“The hierarchical Bayesian approach is an intermediate method compared to the completely pooled model and individualized model, capturing the whole population’s characteristics while allowing individual differences [43].”
From Predicting depressive symptom severity through individuals’ nearby Bluetooth device count data collected by mobile phones: preliminary longitudinal study (2021) · cites this paper as [43]
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Zhang, J., Yin, J., & Wang, R. (2020) · Mathematical Problems in Engineering · doi:10.1155/2020/6068203 · Cited by 52
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Metadata
- Authors
- Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B.
- Affiliations
- Royal Children's Hospital (AU)
- Venue
- Chapman & Hall/CRC eBooks
- Publisher
- Chapman and Hall/CRC
- Published
- 2003-07-29
- OpenAlex
- W2045656233
- Cited by
- 27,276
- References
- 4
- Citations by year
- 2026: 1089 · 2025: 1536 · 2024: 1370 · 2023: 1223 · 2022: 1481 · 2021: 1849 · 2020: 1770 · 2019: 1645 · 2018: 1347 · 2017: 1184 · 2016: 1184 · 2015: 1171 · 2014: 1048 · 2013: 1060 · 2012: 1052
- FWCI
- 48.90
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Chapman & Hall/CRC eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Keywords
- Bayesian analysis, Bayesian inference, computational tools, computer simulation, statistical modeling, model criticism
About these checks
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.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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