On priors with a kullback-leibler property

Journal of the American Statistical Association

Volumn 99, Issue 466, 2004, Pages 404-408

  Walker, Stephen ^a   Damien, Paul ^b   Lenk, Peter ^c  

^a University of Bath   (United Kingdom)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Bayes factor; Decision theory; Exchangeability; Expected utility rule; Kullback Leibler divergence

Indexed keywords

EID: 2942566535     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214504000000386     Document Type: Review

References (26)

1. Barron, A., Schervish, M. J., and Wasserman, L. (1999), "The Consistency of Distributions in Nonparametric Problems," The Annals of Statistics, 27, 536-561.
2. Bernardo, J. M., and Smith, A. F. M. (1994), The Bayesian Theory, New York: Wiley.
3. Billingsley, P. (1968), Convergence of Probability Measures, New York: Wiley.
4. de Groot, M. (1970), Optimal Statistical Decisions, New York: McGraw-Hill.
5. Dey, D., Sinha, D., and Müller, P. (1998), Practical Nonparametric and Semi-parametric Bayesian Statistics, New York: Springer-Verlag.
6. Draper, D. (1995), "Assessment and Propagation of Model Uncertainty" (with discussion), Journal of the Royal Statistical Society, Ser. B, 57, 45-97.
7. _ (1999), Discussion of "Bayesian Nonparametric Inference for Random Distributions and Related Functions," by S. G. Walker, P. Damien, P. W. Laud, and A. F. M. Smith, Journal of the Royal Statistical Society, Ser. B, 61, 485-527.
8. _ (2003), "Three-Fold Cross-Validation: Bayesian Model Choice via Out-of-Sample Predictive Calibration," technical report, University of California Santa Cruz, Dept. of Applied Mathematics and Statistics.
9. Efron, B., and Tibshirani, R. (1996), "Using Specially Designed Exponential Families for Density Estimation," The Annals of Statistics, 24, 2431-2461.
10. Gelfand, A. E., and Dey, D. K. (1994), "Bayesian Model Choice: Asymptotics and Exact Calculations," Journal of the Royal Statistical Society, Ser. B, 56, 501-514.
11. Ghosal, S., Ghosh, J. K., and Ramamoorthi, R. V. (1999), "Posterior Consistency of Dirichlet Mixtures in Density Estimation," The Annals of Statistics, 27, 143-158.
12. Grenander, U. (1981), Abstract Inference, New York: Wiley.
13. Hirshleifer, J., and Riley, J. G. (1992), The Analysis of Uncertainty and Information, Cambridge, U.K.: Cambridge University Press.
14. Lavine, M. (1992), "Some Aspects of Pólya Tree Distributions for Statistical Modelling," The Annals of Statistics, 20, 1222-1235.
15. Lenk, P. (2003), "The Bayesian Semiparametric Density Estimation and Model Verification Using a Logistic-Gaussian Process," Journal of Computational and Graphical Statistics, 12, 548-565.
16. Lindley, D. V. (1985), Making Decisions (2nd ed.), New York: Wiley.
17. Lindsey, J. K. (1999), "Some Statistical Heresies," The Statistician, 48, 1-40.
18. Petrone, S., and Wasserman, L. (2002), "Consistency of Bernstein Polynomial Posteriors," Journal of the Royal Statistical Society, Ser. B, 64, 79-100.
19. Schwartz, L. (1965), "On Bayes Procedures," Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 4, 10-26.
20. Stone, C. J. (1990), "Large-Sample Inference for Log-Spline Models," The Annals of Statistics, 18, 717-741.
21. Stone, C. J., Hansen, M. H., Kooperberg, C., and Truong, Y. K. (1997), "Polynomial Splines and Their Tensor Products in Extended Linear Models," The Annals of Statistics, 25, 1371-1470.
22. Von Neumann, J., and Morgenstern, O. (1947), Theory of Games and Economic Behavior (2nd ed.), Princeton, NJ: Princeton University Press.
23. Walker, S. G. (2003), "On Sufficient Conditions for Hellinger Consistency," Biometrika, 90, 482-488.
24. Walker, S. G., Damien, P., Laud, P. W., and Smith, A. F. M. (1999), "Bayesian Nonparametric Inference for Random Distributions and Related Functions" (with discussion), Journal of the Royal Statistical Society, Ser. B, 61, 485-527.
25. Wasserman, L. (1998), "Asymptotic Properties of Nonparametric Bayesian Procedures," in Practical Nonparametric and Semiparametric Bayesian Statistics, eds. D. Dey, P. Müller, and D. Sinha, New York, Springer-Verlag, pp. 293-304.
26. Whittle, P. (1958), "On the Smoothing of Probability Density Functions," Journal of the Royal Statistical Society, Ser. B, 20, 334-343.