Coverage probability bias, objective Bayes and the likelihood principle

Biometrika

Volumn 88, Issue 3, 2001, Pages 657-675

  Sweeting, Trevor J ^a  

^a UNIVERSITY OF SURREY   (United Kingdom)

Author keywords

Approximate Bayesian inference; Coverage probability bias; Higher order asymptotics; Likelihood principle; Objective Bayes

Indexed keywords

EID: 0142178799     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/88.3.657     Document Type: Article

References (27)

1. BARNDORFF-NIELSEN, O. E. (1986). Inference on full or partial parameters based on the standardised signed log likelihood ratio. Biometrika 73, 307-22.
2. BARNDORFF-NIELSEN, O. E. & CHAMBERLAIN, S. R. (1991). An ancillary invariant modification of the signed log likelihood ratio. Scand. J. Statist. 18, 341-52.
3. BARNDORFF-NIELSEN, O. E. & Cox, D. R. (1984). The effect of sampling rules on likelihood statistics. Int. Statist. Rev. 52, 309-26
4. BARNDORFF-NIELSEN, O. E. & Cox, D. R. (1994). Inference and Asymptotics. London: Chapman and Hall.
5. BERNARDO, J. M. & RAMôN, J. M. (1998). An introduction to Bayesian reference analysis: inference on the ratio of multinomial parameters. Statistician 47, 101-35.
6. Cox, D. R. & REID, N. (1987). Parameter orthogonality and approximate conditional inference (with Discussion). J. R. Statist. Soc. B 49, 1-39.
7. DATTA, G. S., MUKERJEE, R., GHOSH, M. & SWEETING, T. J. (2000). Bayesian prediction with approximate frequentist validity. Ann. Statist. 28, 1414-26.
8. DAWID, A. P. (1991). Fisherian inference in likelihood and prequential frames of reference (with Discussion). J. R. Statist. Soc. B 53, 79-109.
9. DiCiccio, T. J. & MARTIN, M. A. (1993). Simple modifications for signed roots of likelihood ratio statistics. J. R. Statist. Soc. B 55, 305-16
10. GHOSAL, S. (1999). Probability matching priors for non-regular cases. Biometrika 86, 956-64.
11. GHOSH, J. K. & MUKERJEE, R. (1992a). Bayesian and frequentist Bartlett corrections for likelihood ratio and conditional likelihood ratio tests. J. R. Statist. Soc. B 54, 867-75.
12. GHOSH, J. K. & MUKERJEE, R. (1992b). Non-informative priors (with Discussion). In Bayesian Statistics 4, Ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, pp. 195-210. Oxford University Press.
13. HARTIGAN, J. A. (1966). Note on the confidence-prior of Welch and Peers. J. R. Statist. Soc. B 28, 55-6.
14. KASS, R. E. & WASSERMAN, L. (1996). The selection of prior distributions by formal rules. J. Am. Statist. Assoc. 91, 1343-70.
15. MUKERJEE, R. & GHOSH, J. K. (1997). Second-order probability matching priors. Biometrika 84, 970-5.
16. NICOLAOU, A. (1993). Bayesian intervals with good frequency behaviour in the presence of nuisance param-eters. J. R. Statist. Soc. B 55, 377-90.
17. PIERCE, D. A. (1999). On the relation between frequency inference and likelihood. Bull. Int. Statist. Inst., 52nd Session of the ISI, 58, 223-6.
18. PIERCE, D. A. & PETERS, D. (1994). Higher-order asymptotics and the likelihood principle: one parameter models. Biometrika 81, 1-10.
19. SEVERINI, T. A. (1993). Bayesian interval estimates which are also confidence intervals. J. R. Statist. Soc. B 55, 533-40.
20. STEIN, C. M. ( 1985). On the coverage probability of confidence sets based on a prior distribution. In Sequential Methods in Statistics, Banach Center Publications, 16, Ed. R. Zielinski, pp. 485-514. Warsaw: PWN-Polish Scientific.
21. SWEETING, T. J. (1995a). A framework for Bayesian and likelihood approximations in statistics. Biometrika 82, 1-23.
22. SWEETING, T. J. (1995b). A Bayesian approach to approximate conditional inference. Biometrika 82, 25-36.
23. SWEETING, T. J. (1996). Approximate Bayesian computation based on signed roots of log-density ratios (with Discussion). In Bayesian Statistics 5, Ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, pp. 427-44. Oxford University Press.
24. SWEETING, T. J. (1999). On the construction of Bayes-confidence regions. J. R. Statist. Soc. B 61, 849-61.
25. TIBSHIRANI, R. J. (1989). Noninformative priors for one parameter of many. Biometrika 76, 604-8.
26. WELCH, B. L. & PEERS, H. W. (1963). On formulae for confidence points based on integrals of weighted likelihoods. J. R. Statist. Soc. B 35, 318-29.
27. WOODROOFE, M. (1986). Very weak expansions for sequential confidence levels. Ann. Statist. 14, 1049-67.