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Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives

Publication ,  Journal Article
Berger, JO; Guglielmi, A
Published in: Journal of the American Statistical Association
March 1, 2001

Testing the fit of data to a parametric model can be done by embedding the parametric model in a nonparametric alternative and computing the Bayes factor of the parametric model to the nonparametric alternative. Doing so by specifying the nonparametric alternative via a Polya tree process is particularly attractive, from both theoretical and methodological perspectives. Among the benefits is a degree of computational simplicity that even allows for robustness analyses to be implemented. Default (nonsubjective) versions of this analysis are developed herein, in the sense that recommended choices are provided for the (many) features of the Polya tree process that need to be specified. Considerable discussion of these features is also provided to assist those who might be interested in subjective choices. A variety of examples involving location–scale models are studied. Finally, it is shown that the resulting procedure can be viewed as a conditional frequentist test, resulting in data-dependent reported error probabilities that have a real frequentist interpretation (as opposed to p values) in even small sample situations. © 2001 American Statistical Association.

Duke Scholars

Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

March 1, 2001

Volume

96

Issue

453

Start / End Page

174 / 184

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics
 

Citation

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ICMJE
MLA
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Berger, J. O., & Guglielmi, A. (2001). Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives. Journal of the American Statistical Association, 96(453), 174–184. https://doi.org/10.1198/016214501750333045
Berger, J. O., and A. Guglielmi. “Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives.” Journal of the American Statistical Association 96, no. 453 (March 1, 2001): 174–84. https://doi.org/10.1198/016214501750333045.
Berger JO, Guglielmi A. Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives. Journal of the American Statistical Association. 2001 Mar 1;96(453):174–84.
Berger, J. O., and A. Guglielmi. “Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives.” Journal of the American Statistical Association, vol. 96, no. 453, Mar. 2001, pp. 174–84. Scopus, doi:10.1198/016214501750333045.
Berger JO, Guglielmi A. Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives. Journal of the American Statistical Association. 2001 Mar 1;96(453):174–184.

Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

March 1, 2001

Volume

96

Issue

453

Start / End Page

174 / 184

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics