Bayesian Inference Under Partial Prior Information (original) (raw)

Abstract

Partial prior information on the marginal distribution of an observable random variable is considered. When this information is incorporated into the statistical analysis of an assumed parametric model, the posterior inference is typically non-robust so that no inferential conclusion is obtained. To overcome this difficulty a method based on the standard default prior associated to the model and an intrinsic

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (30)

  1. Berger, J. O. (1994). An overview of robust Bayesian analysis (with discussion). Test 3, 5-125.
  2. Berger, J. O. & Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 91, 109-122.
  3. Berger, J. O. & Pericchi, L. R. (1997a). On the justification of default and intrinsic Bayes factor. In Modelling and prediction (eds J. C. Lee, W. O. Johnson, A. Zellner), 276-293. Springer-Verlag, New York.
  4. Berger, J. O. & Pericchi, L. R. (1997b). On criticisms and comparisons of default Bayes factors for model selection and hypothesis testing (with discussion). In Proceedings of the Workshop on Models Selection (ed. W. Racugno) 1-49. Bologna, Pitagora Editrice.
  5. Betro`, B. & Guglielmi, A. (1996). Methods for global prior robustness under generalized moment conditions. In Bayesian robustness (eds J. O. Berger, B. Betro`, F. Ruggeri, E. Moreno, L. Pericchi & L. Wasserman), Vol. 29, 3-20. IMS Lecture Notes-Monograph Series.
  6. Betro`, B. & Guglielmi, A. (2000). Numerical robust Bayesian analysis under generalized moment conditions. In Robust Bayesian analysis (eds D. Rios & F. Ruggeri), 273-294. Springer-Verlag, New York.
  7. Betro`, B., Meczarski, M. & Ruggeri, F. (1994). Robust Bayesian analysis under generalized moment conditions. J. Statist. Plann. Inference 41, 257-266.
  8. Chaloner, K. (1996). The elicitation of prior distributions. In Case studies in Bayesian biostatistics (eds D. Berry, et al.) Dekker, New York.
  9. Cooke, R. M. (1991). Expert in uncertainty: opinion and subjective probability in science. Oxford University Press, New York.
  10. Efron, B. (1996). Empirical Bayes methods for combining likelihoods (with discussion). J. Amer. Statist. Assoc. 91, 538-565.
  11. Gustafson, P. & Wasserman, L. (1995). Local sensitivity diagnostic for Bayesian inference. Ann. Statist. 23, 2153-2167.
  12. Kadane, J. B. & Wolfson, L. J. (1998). Experiences in elicitation. The Statistician 47, 3-19.
  13. Kemperman, J. H. B. (1983). On the role of duality on the theory of moments. In Semi-infinite programming and applications (eds A. V. Fiacco and K. O. Kortanek) Vol. 215, 63-92, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, New York.
  14. Kemperman, J. H. B. (1989). Geometry of the moment problem. Proc. Symp. Appl. Math. 37, 16-53.
  15. Liseo, B., Moreno, E. & Salinetti, G. (1996). Bayesian robustness for classes of bidimensinal priors with given marginals (with discussion). In Bayesian Robustness (eds J. O. Berger, B. Betro´, F. Ruggeri, E. Moreno, L. Pericchi & L. Wasserman). Vol. 29, 103-120. IMS Lecture Notes-Monograph Series.
  16. Meyer, M. & Booker, J. (1991). Knowledge-based expert systems, Vol. 5, Eliciting in quantitative risk and policy analysis. Cambridge University Press, New York.
  17. Moreno, E. (2000). Global Bayesian robustness. In Bayesian robustness (eds D. Rios & F. Ruggeri), 5-37. Springer-Verlag, New York.
  18. Moreno, E. & Liseo, B. (2003). Default priors for testing the number of components of a mixture. J. Statist. Plann. Inference 111, 129-142.
  19. Moreno, E. & Pericchi, L. R. (1993). On e-contaminated priors with quantile and piece-wise constraints. Comm. Statist. Theory Methods 22, 7, 1963-1978.
  20. Moreno, E., Bertolino, F. & Racugno, W. (1998). An intrinsic limiting procedure for model selection and hypotheses testing. J. Amer. Statist. Assoc. 93, 1451-1460.
  21. Moreno, E., Bertolino, F. & Racugno, W. (1999). Default Bayesian analysis of the Behrens-Fisher problem. J. Statist. Plann. Inference 81, 323-333.
  22. O'Hagan, A. (1998). Eliciting expert beliefs in substantial practical applications. The Statistician 47, 21-35.
  23. Pe´rez, J. M. (1998). Development of expected posterior prior distributions. PhD Thesis, Purdue University.
  24. Pe´rez, J. M. & Berger, J. O. (1999). Default analysis for mixture models using expected posterior prior. Technical Report, Universidad Simo´n Bolivar. Caracas.
  25. Pe´rez, J. M. & Berger, J. O. (2000). Expected posterior distribution for model selection. Tech. Rep. 00-08. Duke University, ISDS.
  26. Shui, C. (1996). Default Bayesian analysis of mixture models. PhD Thesis, Purdue Univerity.
  27. Shymalkumar, D. N. (1996). Cyclic I 0 projections and its applications in statistics. Tech. Rep. 96-24. Department of Statistics, Purdue University.
  28. Salinetti, G. (1994). Discussion to Berger. Test 3, 5-125.
  29. Scand J Statist 30
  30. Winkler, R. L. (1980). Prior information, predictive distributions, and Bayesian model-building. In Bayesian analysis in econometrics and statistics (ed. A. Zellner), 95-109, North-Holland, Amsterdam.