Unified frequentist and bayesian testing of a precise hypothesis

Statistical Science

Volumn 12, Issue 3, 1997, Pages 133-148

  Berger, J O ^a   Boukai, B ^b   Wang, Y ^b  

^a DUKE UNIVERSITY   (United States)

^b INDIANA UNIVERSITY   (United States)

Author keywords

Bayes factor; Composite hypothesis; Conditional test; Error probabilities; Likelihood ratio

Indexed keywords

EID: 0005256006     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1030037904     Document Type: Article

References (26)

1. Berger, J. O., Brown, L. D. and Wolpert, R. L. (1994). A unified conditional frequentist and Bayesian test for fixed and sequential simple hypothesis testing. Ann. Statist. 22 1787-1807.
2. Berger, J. O. and Delampady, M. (1987). Testing precise hypotheses. Statist. Sci. 3 317-352.
3. Berger, J. O. and Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 91 109-122.
4. Berger, J. O. and Sellke, T. (1987). Testing a point null hypothesis: the irreconcilability of P-values and evidence. J. Amer. Statist. Assoc. 82 112-122.
5. Berger, J. O. and Wolpert, R. L. (1988). The Likelihood Principle, 2nd ed. IMS, Hayward, CA.
6. Bernardo, J. M. (1980). A Bayesian analysis of classical hypothesis testing. In Bayesian Statistics (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 605-647. Valencia Univ. Press.
7. Brown, L. D. (1978). A contribution to Kiefer’s theory of conditional confidence procedures. Ann. Statist. 6 59-71.
8. Brownie, C. and Keifer, J. (1977). The ideas of conditional confidence in the simplest setting. Comm. Statist. Theory Methods 6 691-751.
9. Casella, G. and Berger, R. (1987). Reconciling Bayesian and frequentist evidence in the one-sided testing problem. J. Amer. Statist. Assoc. 82 106-111.
10. Chatterjee, s. K. and Chattopadhyay, G. (1993). Detailed statistical inference-multiple decision problems. Calcutta Statist. Assoc. Bull. 43 155-180.
11. Chernoff, H. (1972). Sequential Analysis and Optimal Design. SIAM, Philadelphia.
12. Delampady, M. and Berger, J. O. (1990). Lower bounds on Bayes factors for the multinomial distribution, with application to chi-squared tests of fit. Ann. Statist. 18 1295-1316.
13. Edwards, W., Lindman, H. and Savage, L. J. (1963). Bayesian statistical inference for psychological research. Psychological Review 70 193-242.
14. Evans, M. (1994). Bayesian inference procedures derived via the concept of relative surprise. Technical report, Dept. Statistics, Univ. Toronto.
15. Fisher, L. D. and Van Belle, G. (1993). Biostatistics: A Methodology for the Health Sciences. Wiley, New York.
16. Good, I. J. (1992). The Bayesian/Non-Bayesian compromise: a brief review. J. Amer. Statist. Assoc. 87 597-606.
17. Hwang, J. T., Casella, G., Robert, C., Wells, M. T. and Farrell, R. (1992). Estimation of accuracy in testing. Ann. Statist. 20 490-509.
18. Jeffreys, H. (1961). Theory of Probability. Oxford Univ. Press.
19. Kiefer, J. (1975). Conditional confidence approach in multi decision problems. In Multivariate Analysis IV (P. R. Krishnaiah, ed.) 143-158. Academic Press, New York.
20. Kiefer, J. (1976). Admissibility of conditional confidence procedures. Ann. Math. Statist. 4 836-865.
21. Kiefer, J. (1977). Conditional confidence statements and confidence estimators (with discussion). J. Amer. Statist. Assoc. 72 789-827.
22. O’Hagan, A. (1995). Fractional Bayes factors for model comparisons. J. Roy. Statist. Soc. Ser. B 57 99-138.
23. Pappas, T. and Mitchell, C. A. (1985). Effects of seismic stress on the vegetative growth of Glycine max (L.) Merr. cv. Wells II. Plant, Cell and Environment 8 143-148.
24. Robert, C. p. and Caron, N. (1995). Noninformative Bayesian testing and neutral Bayes factors. Technical report, CREST, INSEE, Paris.
25. Schaafsma, W. and van DER Meulen, A. E. (1993). Assessing weights of evidence for discussing classical statistical hypotheses. Statist. Decisions 11 201-220.
26. Wolpert, R. L. (1995). Testing simple hypotheses. In Studies in Classification, Data Analysis, and Knowledge Organization (H. H. Bock and W. Polasek, eds.) 7 289-297. Springer, Berlin.