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

  • Gauri Sankar Datta
  • Rahul Mukerjee
Bayesian Approach


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.

Key words and phrases

Bayesian prediction frequentist validity highest predictive density region noninformative prior posterior quantile regression shrinkage argument 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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.MathSciNetGoogle Scholar
  2. Cox, D. R. and Reid, N. (1987). Parameter orthogonality and approximate conditional inference (with discussion).J. Roy. Statist. Soc. Ser. B,49, 1–39.MathSciNetGoogle Scholar
  3. Datta, G.S., Mukerjee, R., Ghosh, M. and Sweeting, T. J. (2000). Bayesian prediction with approximate frequentist validity,Ann. Statist.,28, 1414–1426.CrossRefMathSciNetGoogle Scholar
  4. 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.CrossRefMathSciNetGoogle Scholar
  5. 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
  6. Johnson, R. A. (1970). Asymptotic expansions associated with posterior distributions,Ann. Math. Statist.,41, 851–864.MathSciNetGoogle Scholar
  7. Komaki, F. (1996). On asymptotic properties of predictive distributions,Biometrika,83, 299–314.CrossRefMathSciNetGoogle Scholar
  8. Mukerjee, R. and Reid, N. (1999). On a property of probability matching priors: Matching the alternative coverage probabilities,Biometrika,86, 333–340.CrossRefMathSciNetGoogle Scholar
  9. Mukerjee, R. and Reid, N. (2000). On the Bayesian approach for frequentist computations, BrazilianJournal of Probability and Statistics (to appear).Google Scholar
  10. Tishirani, R. (1989). Noninformative priors for one parameter of many,Biometrika,76, 604–608.CrossRefMathSciNetGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics 2003

Authors and Affiliations

  • Gauri Sankar Datta
    • 1
  • Rahul Mukerjee
    • 2
  1. 1.Department of StatisticsUniversity of GeorgiaAthensUSA
  2. 2.Indian Institute of ManagementCalcuttaIndia

Personalised recommendations