Skip to main content
SpringerLink
Log in

Probability matching priors for predicting a dependent variable with application to regression models

  • Bayesian Approach
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

In a Bayesian setup, we consider the problem of predicting a dependent variable given an independent variable and past observations on the two variables. An asymptotic formula for the relevant posterior predictive density is worked out. Considering posterior quantiles and highest predictive density regions, we then characterize priors that ensure approximate frequentist validity of Bayesian prediction in the above setting. Application to regression models is also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bickel, P. J. and Ghosh, J. K. (1990). A decomposition for the likelihood ratio statistic and the Bartlett correction—a Bayesian argument,Ann. Statist.,18, 1070–1090.

    MathSciNet  Google Scholar 

  • Cox, D. R. and Reid, N. (1987). Parameter orthogonality and approximate conditional inference (with discussion).J. Roy. Statist. Soc. Ser. B,49, 1–39.

    MathSciNet  Google Scholar 

  • Datta, G.S., Mukerjee, R., Ghosh, M. and Sweeting, T. J. (2000). Bayesian prediction with approximate frequentist validity,Ann. Statist.,28, 1414–1426.

    Article  MathSciNet  Google Scholar 

  • Ghosh, J.K. and Mukerjee, R. (1993). Frequentist validity of highest posterior density regions in the multiparameter case,Ann. Inst. Statist. Math.,45, 293–302.

    Article  MathSciNet  Google Scholar 

  • Ghosh, M. and Mukerjee, R. (1998). Recent developments on probability matching priors,Applied Statistical Science III (eds. S. E. Ahmed, M. Ahsanullah and B. K. Sinha), 227–252, Nova Science Publishers, New York.

    Google Scholar 

  • Johnson, R. A. (1970). Asymptotic expansions associated with posterior distributions,Ann. Math. Statist.,41, 851–864.

    MathSciNet  Google Scholar 

  • Komaki, F. (1996). On asymptotic properties of predictive distributions,Biometrika,83, 299–314.

    Article  MathSciNet  Google Scholar 

  • Mukerjee, R. and Reid, N. (1999). On a property of probability matching priors: Matching the alternative coverage probabilities,Biometrika,86, 333–340.

    Article  MathSciNet  Google Scholar 

  • Mukerjee, R. and Reid, N. (2000). On the Bayesian approach for frequentist computations, BrazilianJournal of Probability and Statistics (to appear).

  • Tishirani, R. (1989). Noninformative priors for one parameter of many,Biometrika,76, 604–608.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Georgia, 30602-1952, Athens, GA, USA

    Gauri Sankar Datta

  2. Indian Institute of Management, Post Box No. 16757, 700 027, Calcutta, India

    Rahul Mukerjee

Authors
  1. Gauri Sankar Datta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rahul Mukerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Datta, G.S., Mukerjee, R. Probability matching priors for predicting a dependent variable with application to regression models. Ann Inst Stat Math 55, 1–6 (2003). https://doi.org/10.1007/BF02530481

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02530481

Key words and phrases

Search

Navigation