Bayes Estimates for the Linear Model
Abstract
Summary The usual linear statistical model is reanalyzed using Bayesian methods and the concept of exchangeability. The general method is illustrated by applications to two-factor experimental designs and multiple regression.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Lindley and Smith (1972) showed that allowing the data to estimate the prior variance of parameters is essentially what ridge regression does for linear regression.
“Lindley and Smith (1972) showed that this is essentially what ridge regression does for linear regression”
From Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors (1999) · cites this paper as Lindley and Smith (1972)
Cited by
Sorted by citations
Bayesian Measures of Model Complexity and Fit
Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00353 · Cited by 151 · see citing works
Cross validatory choice and assessment of statistical predictions
Stone, M. (1974) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1974.tb00994.x · Cited by 10,881 · see citing works
Pooled Mean Group Estimation of Dynamic Heterogeneous Panels
Pesaran, M. H., Shin, Y., & Smith, R. P. (1999) · Journal of the American Statistical Association · doi:10.1080/01621459.1999.10474156 · Cited by 6,683 · see citing works
Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999) · Statistical Science · doi:10.1214/ss/1009212519 · Cited by 4,118 · see citing works
Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems
Harville, D. A. (1977) · Journal of the American Statistical Association · doi:10.1080/01621459.1977.10480998 · Cited by 2,667 · see citing works
Parametric empirical Bayes inference: theory and applications
Morris, C. N. (1983) · Journal of the American Statistical Association · doi:10.1080/01621459.1983.10477920 · Cited by 1,448 · see citing works
Ozone and short-term mortality in 95 US urban communities, 1987–2000
Bell, M. L. (2004) · JAMA · doi:10.1001/jama.292.19.2372 · Cited by 1,202 · see citing works
Risk of Alzheimer's disease and duration of NSAID use
Stewart, W. F., Kawas, C., Corrada, M., & Metter, E. J. (1997) · Neurology · doi:10.1212/wnl.48.3.626 · Cited by 1,132 · see citing works
Genomic-Assisted Prediction of Genetic Value With Semiparametric Procedures
Gianola, D., Fernando, R. L., & Stella, A. (2006) · Genetics · doi:10.1534/genetics.105.049510 · Cited by 450 · see citing works
Dementia after ischemic stroke: A population-based study in Rochester, Minnesota (1960-1984)
Kokmen, E., Whisnant, J. P., O'Fallon, W. M., Chu, C.-P., & Beard, C. M. (1996) · Neurology · doi:10.1212/wnl.46.1.154 · Cited by 434 · see citing works
Bayesian probabilistic population projections for all countries
Raftery, A. E., Li, N., Ševčíková, H., Gerland, P., & Heilig, G. K. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1211452109 · Cited by 298 · see citing works
Bentall, R. P., Rowse, G., Shryane, N., Kinderman, P., Howard, R., Blackwood, N., Moore, R., & Corcoran, R. (2009) · Archives of General Psychiatry · doi:10.1001/archgenpsychiatry.2009.1 · Cited by 295 · see citing works
Empirical bayes meta-analysis.
Raudenbush, S. W., & Bryk, A. S. (1985) · Journal of Educational Statistics · doi:10.3102/10769986010002075 · Cited by 299 · see citing works
Probabilistic projections of the total fertility rate for all countries
Alkema, L., Raftery, A. E., Gerland, P., Clark, S. J., Pelletier, F., Buettner, T., & Heilig, G. K. (2011) · Demography · doi:10.1007/s13524-011-0040-5 · Cited by 248 · see citing works
Bayesian Computation and Model Selection Without Likelihoods
Leuenberger, C., & Wegmann, D. (2010) · Genetics · doi:10.1534/genetics.109.109058 · Cited by 175 · see citing works
- Authors
- Lindley, D. V., & Smith, A. F. M.
- Affiliations
- University College London (GB)
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1972-09-01
- Volume
- 34
- Issue
- 1
- Pages
- 1-18
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W128740895
- Cited by
- 2,025
- References
- 0
- Citations by year
- 2026: 23 · 2025: 36 · 2024: 23 · 2023: 37 · 2022: 35 · 2021: 49 · 2020: 34 · 2019: 41 · 2018: 38 · 2017: 41 · 2016: 55 · 2015: 75 · 2014: 71 · 2013: 45 · 2012: 89
- FWCI
- 27.65
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- Bayesian estimation, linear statistical models, exchangeability, multiple linear regression, prior distributions
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 ›
Are you an author, or do you see a problem with this page? Request a review
