Bayesian perspectives on multiple comparisons

Journal of Statistical Planning and Inference

Volumn 82, Issue 1-2, 1999, Pages 215-227

  Berry, Donald A ^a   Hochberg, Yosef ^b  

^a DUKE UNIVERSITY   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Dirichlet process prior; Duncan's procedure; Hierarchical priors; Quasi Bayesian

Indexed keywords

EID: 0033472376     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(99)00044-0     Document Type: Article

References (45)

1. Antoniak, C.E., 1974. Mixtures of Dirichlet processes with application to Bayesian nonparametric problems. Ann. Statist. 2, 1152-1174.
2. Benjamini, Y., Hochberg, Y., 1995. Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Roy. Statist. Soc. B. 57 (1), 289-300.
3. Benjamini, Y., Hochberg, Y., 1997. Weighted multiple comparison procedures. Scand. J. Statist., in Press.
4. Benjamini, Y., Liu, W., 1999. A stepdown multiple hypotheses testing procedure that controls the false discovery rate under independence. J. Statist. Plann. Inference 82, 163-170 (this issue).
5. Berger, J.O., 1984. In: Kadane, J.B. (Ed.), Robustness of Bayesian Analysis. North-Holland, Amsterdam (with discussion).
6. Berger, J.O., 1986. Statistical Decision Theory and Bayesian Analysis, Second Ed., Springer, New York.
7. Berger, J.O., Berry, D.A., 1988. Statistical analysis and the illusion of objectivity. The Amer. Sci. 76, 159-165.
8. Berger, J.O., Wolpert, R.L., 1984. The Likelihood Principle. Institute of Mathematical Statistics, Hayward, California.
9. Bernardo, J.M., Smith, A.F.M., 1994. Bayesian Theory. Wiley, Chichester.
10. Berry, D.A., 1988. Multiple comparisons, multiple tests, and data dredging: A Bayesian perspective (with discussion). In: Bernardo, J.M., DeGroot, M.H., Lindley, D.V., Smith, A.F.M. (Eds.), Bayesian Statistics, Vol. 3. Oxford University Press. Oxford, England, pp. 79-94.
11. Berry, D.A., 1990. Subgroup analyses. Biometrics 47, 1227-1230.
12. Berry, D.A., 1996. Statistics, A Bayesian Perspective. Duxbury Press, Belmont, CA.
13. Berry, D.A., Christensen, R.R., 1979. Empirical Bayes estimation of a binomial parameter via mixtures of Dirichlet processes. Ann. Statist. 7, 558-568.
14. Berry, D.A., Stangl, D.K., 1996. Bayesian Biostatistics. Marcel Dekker. New York.
15. Bohrer, R., 1979. Multiple three-decision rules for parametric signs. J. Amer. Statist. Assoc. 74, 432-437.
16. Breslow, N., 1990. Biostatistics and Bayes. Statist. Sci. 5, 269-283.
17. Carlin, B., Louis, T., 1997. Bayes and Empirical Bayes Methods. Chapman & Hall, London.
18. Carmer, S.G., Walker, W.M., 1982. Baby bear's dilemma: A statistical tale. Agron. J. 74, 122-124.
19. DuMouchel, W., 1988. A Bayesian model and graphical elicitation procedure for multiple comparisons. In: Bernardo, J.M., DeGroot, M.H., Lindley, D.V., Smith, A.F.M. (Eds.), Bayesian Statistics, vol. 3. Oxford University Press. Oxford, England.
20. DuMouchel, W., 1989. In: Berry, D.A. (Ed.), Bayesian Metaanalysis, Statistical Methodology in the Pharmaceutical Sciences. Marcel Dekker, New York, pp. 509-529.
21. Duncan, D.B., 1965. A Bayesian approach to multiple comparisons. Technometrics 7, 171-222.
22. Ferguson, T.S., 1973. A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 209-230.
23. Freedman, L., 1996. Bayesian statistical methods - A natural way to assess clinical evidence. British Med. J. 313, 569-570.
24. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B., 1995. Bayesian Data Analysis. Chapman & Hall, London.
25. Gilks, W.R., Richardson, S., Spiegelhalter, D.J., 1996. Markov Chain Monte Carlo in Practice. Chapman & Hall, London.
26. Good, I.J., 1971. 46656 kinds of Bayesians. Amer. Statist. 25, 62-63.
27. Good, I.J., 1988. Scientific method and statistics. Encyclopedia of Statistical Sciences, vol. 8, pp. 291-304.
28. Gopalan, R., Berry, D.A., 1998. Bayesian multiple comparisons using Dirichlet process priors. J. Amer. Statist. Assoc. 93 (443), 1130-1139.
29. Grechanovsky, E., Pinsker, I., 1999. A general approach to stepup multiple test procedures for free-combination families. J. Statist. Plann. Inference 82, 34-54 (this issue).
30. Hochberg, Y., Tamhane, C.A., 1987. Multiple Comparison Procedures. Wiley, New York.
31. Lehmann, E.L., 1957. A theory of some multiple decision problems, (parts I and II), Ann. Math. Statist. 28, 1-25 and 547-572.
32. Lewis, C., 1984. Multiple Comparisons: Fisher Revisited. University of Groningen, Netherlands, unpublished manuscript.
33. Lindley, D.V., 1971. Discussion on papers by Wynn, Bloomfield, O'neill and Wetherill. J. Roy. Statist. Soc. Ser. B 33, 218-241.
34. Light, R.J., Pillemer, D.B., 1984. Summing up. The Science of Reviewing Research. Harvard University Press, Cambridge.
35. Miller, R.G., 1966. Simultaneous Statistical Inference, First Ed. McGraw-Hill. New York.
36. O'Brien, P.C., 1983. The appropriateness of analysis of variance and multiple-comparison procedures. Biometrics 39, 787-788.
37. O'Neill, R.T., Wetherill, G.B., 1971. The present state of multiple comparison methods (with discussion). J. Roy. Statist. Soc. Ser. B 33, 218-241.
38. Rothman, K.J., 1990. No adjustments are needed for multiple comparisons. Epidemiology 1, 43-46.
39. Shaffer, P.J., 1999. A semi-Bayesian study of Duncan's Bayesian multiple comparison procedure. J. Statist. Plann. Inference 82, 197-213 (this issue).
40. Tamhane, A.C., Dunnett, C.W., 1999. Stepwise multiple test procedures with biometric applications. J. Statist. Plann. Inference 82, 55-68 (this issue).
41. Tukey, J., 1952. The Problem of Multiple Comparisons. Unpublished manuscript.
42. Tukey, J.W., 1991. The philosophy of multiple comparisons. Statist. Sci. 6, 100-116.
43. Waller, R.A., Duncan, D.B., 1969. A Bayes rule for the symmetric multiple comparison problem. J. Amer. Statist. Assoc. 64, 1484-1503.
44. Westfall, P.H., Johnson, W.O., Utts, J.M., 1997. A Bayesian perspective on the Bonferroni adjustment. Biometrika 84, 419-427.
45. Westfall, P.H., Krishen, A., Young, S.S., 1998. Using prior information to allocate significant levels for multiple endpoints. Statist. Med. 17, 2107-2119.