Student or educator? Sign up with your school email and get 6 months of Pro free.
Cited by 1,007

The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.

The Intrinsic Bayes Factor for Model Selection and Prediction

Berger, James O., Pericchi, Luis R.·1996·Journal of the American Statistical Association

Abstract

In the Bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions, it is typically not possible to utilize standard noninformative (or default) prior distributions. This has led Bayesians to use conventional proper prior distributions or crude approximations to Bayes factors. In this article we introduce a new criterion called the intrinsic Bayes factor, which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual Bayes factors. The criterion can be used for nested or nonnested models and for multiple model comparison and prediction. From another perspective, the development suggests a general definition of a “reference prior” for model comparison.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1080/01621459.1996.10476668

Cites

4 of 4 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 4 references

Research works printed but not linked: 45

  1. 10.1111/j.2517-6161.1991.tb01812.x · DOI · Paper page
  2. Albert , J. H. 1990 . “A Bayesian Test for a Two-Way Contingency Table Using Independence Priors,” . Canadian Journal of Statistics , 14 : 1583 – 1590 .
  3. 10.1093/biomet/65.1.39 · DOI
  4. Berger , J. and Bernardo , J. M. 1992 . “On the Development of the Reference Prior Method,” . In Bayesian Statistics IV , Edited by: Bernardo , J. M. 35 – 60 . London : Oxford University Press . · DOI · Paper page
  5. Berger , J. and Pericchi , L. 1993 . “The Intrinsic Bayes Factor for Model Selection and Prediction,” , Purdue University, Dept. of Statistics . Technical Report 93–43C
  6. Berger , J. and Pericchi , L. 1994 . “The Intrinsic Bayes Factor for Linear Models,” , Purdue University, Dept. of Statistics . Technical Report 94–10C
  7. Berger , J. and Pericchi , L. 1995 . “The Intrinsic Bayes Factor for Linear Models,” . In Bayesian Statistics V , Edited by: Bernardo , J. M. 23 – 42 . London : Oxford University Press .
  8. Berger , J. , Pericchi , L. and Varshavsky , J. 1995 . “An Identity for Linear and Invariant Models, With Application to Non-Gaussian Model Selection,” , Purdue University, Dept. of Statistics . Technical Report 95–7C
  9. 10.1080/01621459.1987.10478397 · DOI · Paper page
  10. 10.1111/j.2517-6161.1979.tb01066.x · DOI · Paper page
  11. 10.1080/01621459.1995.10476635 · DOI · Paper page
  12. 10.1214/aos/1176347750 · DOI
  13. de Vos , A. F. 1993 . “A Fair Comparison Between Regression Models of Different Dimension,” , Amsterdam : The Free University . technical report
  14. Dey , D. K. 1995 . “ Discussion of “The Intrinsic Bayes Factor for Linear Models,” . In Bayesian Statistics V , Edited by: Bernardo , J. M. 43 – 45 . London : Oxford University Press . by J. Berger and L. Pericchi
  15. Dmochowski , J. 1994 . “Intrinsic Priors Via Kullback—Leibler Geometry,” , Purdue University, Dept. of Statistics . Technical Report 94–15
  16. 10.1111/j.2517-6161.1995.tb02015.x · DOI · Paper page
  17. 10.1037/h0044139 · DOI · Paper page
  18. 10.1080/01621459.1979.10481632 · DOI · Paper page
  19. 10.1111/j.2517-6161.1994.tb01996.x · DOI · Paper page
  20. 10.1093/oso/9780198522669.003.0009 · DOI · Paper page
  21. 10.1111/j.2517-6161.1992.tb01443.x · DOI · Paper page
  22. Good , I. J. 1985 . “Weight of Evidence: A Brief Survey,” . In Bayesian Statistics 2 , Edited by: Bernardo , J. M. 249 – 269 . New York : Elsevier .
  23. 10.1214/aos/1176350709 · DOI · Paper page
  24. Haughton , D. and Dudley , R. 1992 . “Information Criteria for Multiple Data Sets and Restricted Parameters,” , Bentley College, Dept. of Mathematics . technical report
  25. Jefferys , W. and Berger , J. 1992 . “Ockham's razor and Bayesian analysis,” . American Scientist , 80 : 64 – 72 .
  26. Jeffreys , H. 1961 . Theory of Probability , London : Oxford University Press .
  27. 10.1080/01621459.1995.10476572 · DOI · Paper page
  28. 10.1080/01621459.1995.10476592 · DOI · Paper page
  29. Lempers , F. B. 1971 . Posterior Probabilities of Alternative Linear Models , Rotterdam : University of Rotterdam Press .
  30. 10.1093/biomet/79.4.663 · DOI
  31. 10.1080/01621459.1988.10478694 · DOI · Paper page
  32. 10.1111/j.2517-6161.1995.tb02017.x · DOI · Paper page
  33. 10.1016/0378-3758(94)90126-0 · DOI
  34. Poirier , D. J. 1985 . “Bayesian Hypothesis Testing in Linear Models With Continuously Induced Conjugate Priors Across Hypotheses,” . In Bayesian Statistics 2 , Edited by: Bernardo , J. M. 711 – 722 . New York : Elsevier .
  35. 10.1080/00401706.1963.10490105 · doi:10.1080/00401706.1963.10490105
  36. Raftery , A. E. 1993 . “Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models,” , University of Washington, Dept. of Statistics . Technical Report 255
  37. Rosenkrantz , S. 1992 . “The Bayes Factor for Model Evaluation in a Hierarchical Poisson Model for Area Counts,” , Ph.D. dissertation University of Washington, Dept. of Biostatistics .
  38. 10.1111/j.2517-6161.1984.tb01302.x · DOI
  39. 10.1214/aos/1176344136 · DOI · Paper page
  40. 10.1111/j.2517-6161.1980.tb01122.x · DOI · Paper page
  41. 10.1093/biomet/67.2.493 · DOI
  42. Spiegelhalter , D. J. and Smith , A. F. M. 1982 . “Bayes Factors for Linear and Log-Linear Models With Vague Prior Information,” . Journal of the Royal Statistical Society , 44 : 377 – 387 . Ser. B
  43. 10.2307/2348514 · DOI
  44. Verdinelli , I. and Wasserman , L. 1995 . “Bayes Factors, Nuisance Parameters, and Imprecise Tests,” . In Bayesian Statistics V , Edited by: Bernardo , J. M. London : Oxford University Press .
  45. Zellner , A. and Siow . 1980 . “Posterior Odds for Selected Regression Hypotheses,” . In Bayesian Statistics 1 , Edited by: Bernardo , J. M. 585 – 603 . Valencia : Valencia University Press .

Cited by

See all 1,007

Metadata

Authors
Berger, J. O., & Pericchi, L. R.
Venue
Journal of the American Statistical Association
Published
1996-03
Volume
91
Issue
433
Pages
109-122
ISSN
  • 0162-1459 (ISSN-L)
  • 1537-274X
OpenAlex
W2101122849
Cited by
1,007
References
4
FWCI
23.75
Type
journal article
Language
en
Open access
closed

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

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: The Intrinsic Bayes Factor for Model Selection and Prediction. https://app.cochat.ai/papers/10.1080/01621459.1996.10476668
The paper
Berger, J. O., & Pericchi, L. R. (1996). The Intrinsic Bayes Factor for Model Selection and Prediction. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1996.10476668

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.