New approaches to Bayesian consistency

Annals of Statistics

Volumn 32, Issue 5, 2004, Pages 2028-2043

  Walker, Stephen ^a,b  

^a UNIVERSITY OF BATH   (United Kingdom)

^b University of Bath   (United Kingdom)

Author keywords

Hellinger consistency; Kullback Leibler consistency; Martingale sequence; Predictive density

Indexed keywords

EID: 4043073169     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053604000000409     Document Type: Article

References (10)

1. BARRON, A. (1988). The exponential convergence of posterior probabilities with implications for Bayes estimators of density functions. Unpublished manuscript.
2. BARRON, A., SCHERVISH, M. J. and WASSERMAN, L. (1999). The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27 536-561.
3. GHOSAL, S., GHOSH, J. K. and RAMAMOORTHI, R. V. (1999). Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27 143-158.
4. LOÈVE, M. (1963). Probability Theory, 3rd ed. Van Nostrand, Princeton, NJ.
5. PETRONE, S. and WASSERMAN, L. (2002). Consistency of Bernstein polynomial posteriors. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 79-100.
6. SCHWARTZ, L. (1965). On Bayes procedures. Z. Wahrsch. Verw. Gebiete 4 10-26.
7. SHEN, X. and WASSERMAN, L. (2001). Rates of convergence of posterior distributions. Ann. Statist. 29687-714.
8. WALKER, S. G. (2003). On sufficient conditions for Bayesian consistency. Biometrika 90 482-488.
9. WALKER, S. G. and GUTIÉRREZ-PEÑA, E. (1999). Robustifying Bayesian procedures (with discussion). In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 685-710. Oxford Univ. Press.
10. WALKER, S. G. and HJORT, N. L. (2001). On Bayesian consistency. J. R. Stat. Soc. Ser. B Stat. Methodol. 63811-821.