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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In an example from Rubin and Gelman et al., the data are compatible with a hierarchical standard deviation of zero but also with values as high as 10 or 20.
“The data are consistent with a standard deviation of 0, but it could also be as high as 10 or 20.”
From Analysis of variance—why it is more important than ever (2005) · cites this paper as Gelman, Carlin, Stern and Rubin [(1995), Chapter 5]
For effects that are unique or in pairs (df=1), the posterior density for σ_m is improper with infinite mass as σ_j→∞, so coefficients in these batches are essentially estimated by maximum likelihood.
“However, for effects that are unique or in pairs [i.e., batches for which (df ) m = 1], the posterior density for the corresponding σ m is improper, with infinite mass in the limit σ j → ∞ [Gelman, Carlin, Stern and Rubin (1995), Exercise 5.8], and so the coefficients β (m) j in these batches are essentially being estimated via maximum likelihood.”
From Analysis of variance—why it is more important than ever (2005) · cites this paper as Gelman, Carlin, Stern and Rubin (1995)
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- Authors
- Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B.
- Venue
- Routledge eBooks
- Publisher
- Routledge
- Published
- 1995-06-01
- OpenAlex
- W4256118999
- Cited by
- 258
- References
- 0
- Citations by year
- 2025: 51 · 2024: 23 · 2023: 22 · 2022: 17 · 2021: 3 · 2020: 7 · 2019: 4 · 2018: 5 · 2017: 2 · 2016: 2 · 2015: 5 · 2014: 6 · 2013: 5 · 2012: 11
- FWCI
- 0.25
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Routledge eBooks (publishedVersion)
- 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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