On the frequentist and Bayesian approaches to hypothesis testing

SORT

Volumn 30, Issue 1, 2006, Pages 3-27

  Moreno, Elías ^a,b   Javier Giron F ^a,b  

^a UNIVERSITY OF GRANADA   (Spain)

^b UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

Bayes factor; Consistency; Intrinsic priors; Loss function; Model posterior probability; p values

Indexed keywords

EID: 33750691991     PISSN: 16962281     EISSN: 20138830     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. New York: Springer-Verlag.
2. Berger, J.O. (1994). An overview of robust Bayesian analysis (with discussion). Test, 3, 5-124.
3. Berger, J.O. and Bernardo, J.M. (1992). On the development of the reference prior method. In Bayesian Statistics 4. J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F:M. Smith, eds. Oxford University Press: Oxford, pp. 35-60.
4. Berger, J.O. and Mortera, J. (1999). Default Bayes factors for nonnested hypothesis testing. Journal of the American Statistical Association, 94, 542-554.
5. Berger, J.O. and Pericchi, L.R. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91, 109-122.
6. Berger, J.O. and Sellke, T. (1987). Testing a point null hypothesis: the irreconcilability of p-values and evidence (with discussion). Journal of the American Statistical Association, 82, 112-139.
7. Bernardo, J.M. and Smith, A.F.M. (1994). Bayesian Theory, New York: Wiley.
8. Box, G.E.P. and Tiao, G.C. (1973). Bayesian Inference in Statistical Analysis. Reading, MA: Addison-Wesley.
9. Cano, J.A., Kessler, M. and Moreno, E. (2004). On intrinsic priors for nonnested models. Test, 13, 445-463.
10. Casella, G. and Berger, R.L. (1987). Reconciling Bayesian and frequentist evidence in the one-sided testing problem. Journal of the American Statistical Association, 82, 106-111.
11. Casella, G. and Berger, R.L. (1990). Statistical Inference. Belmont: Wadsworth.
12. Casella, G. and Moreno, E. (2005). Intrinsic meta analysis of contingency tables, Statistic in Medicine, 24, 583-604.
13. Casella, G. and Moreno, E. (2005). Objective Bayesian variable selection. Journal of the American Statistical Association (to appear).
14. Fisher, R.A. (1936). The fiducial arguments in statistical inference. Annals of Eugenics, 6, 391-422.
15. Girón, F.J., Martínez, L. and Imlahi, L. (1999). A characterization of the Behrens-Fisher distribution with applications to Bayesian inference. Comptes rendus de l'Académie des sciences de Paris, Ser I, 701-706.
16. Girón, F., Martínez, L., Moreno, E. and Torres, F. (2003). Bayesian analysis of matched pairs in the presence of covariates. In Bayesian Statistics 7. J.M.Bernardo et al. (eds.), 553-563, Oxford: Oxford University Press.
17. Girón, F.J., Martínez, L., and Moreno, E. (2003). Bayesian analysis of matched pairs. Journal of Statistical Planning and Inference, 113, 49-66.
18. Girón, F.J., Martínez, M.L., Moreno, E. and Torres, F. (2004). Objective testing procedures in linear models. Calibration of the p-values. Submitted.
19. Girón, F.J., Moreno, E. and Martínez, L. (2005). An objective Bayesian procedure for variable selection in regression. In Advances on distribution theory, order statistics and inference. Eds. N. Balakrishnan et al., Birkhauser Boston, (to appear).
20. Jeffreys, H. (1961). Theory of Probability. London: Oxford University Press.
21. Lempers, F.B. (1971). Posterior Probabilities of Alternative Linear Models. Rotterdam: Rotterdam University Press.
22. Lehman, E. (1986). Testing Statistical Hypotheses, (second edition). New York: Wiley.
23. Lindley, D.V. (1970). An Introduction to Probability and Statistics from a Bayesian Viewpoint (Vol. 2). Cambridge: Cambridge University Press.
24. Miller, A.J. (2002). Subset Selection in Regression. 2nd edition. London: Chapman and Hall.
25. Moreno, E. (1997). Bayes Factor for Intrinsic and Fractional Priors in Nested Models: Bayesian Robustness. IMS Lectures Notes-Monograph Series, 31, 257-270.
26. Moreno, E. (2005). Objective Bayesian analysis for one-sided testing, Test, 14, 181-198.
27. Moreno, E., Bertolino, F. and Racugno, W. (1998). An intrinsic limiting procedure for model selection and hypotheses testing. Journal of the American Statistical Association, 93, 1451-1460.
28. Moreno, E., Bertolino, F. and Racugno, W. (1999). Default Bayesian analysis of the Behrens-Fisher problem. Journal of Statistical Planning and Inference, 81, 323-333.
29. Moreno, E., Bertolino, F. and Racugno, W. (2000). Bayesian model selection approach to analysis of variance under heterocedasticity, Journal of the Royal Statistical Society, Series D (The Statistician), 49, 1-15.
30. Moreno, E., Bertolino, F. and Racugno, W. (2003). Bayesian inference under partial prior information, Scandinavian Journal of Statistics, 30, 565-580.
31. Moreno, E. and Cano J.A. (1989). Testing a point null hypothesis: asymptotic robust Bayesian analysis with respect to the priors given on a subsigma field. International Statistical Review, 57, 221-232.
32. Moreno, E. and Girón, F.J. (2005a). Consistency of Bayes factors for linear models, Comptes rendus de l'Académie des sciences de Paris, Ser I, 911-914.
33. Moreno, E. and Girón, F.J. (2005b). Comparison of Bayesian objective procedures for variable selection in regression. Submitted.
34. Moreno, E., Girón, F.J., and Torres, F. (2003). Intrinsic priors for hypothesis testing in normal regression models. Revista de la Real Academia de Ciencias Serie A,. Mat., 97, 53-61.
35. Moreno, E. and Liseo, B. (2003). A default Bayesian test for the number of components of a mixture. Journal of Statistical Planning and Inference, 111, 129-142.
36. Moreno, E., Torres, F., and Casella, G. (2005). Testing the equality of regression coefficients in heteroscedastic normal regression models. Journal of Statistical Planning and Inference, 131, 117-134.
37. O'Hagan, A. (1995). Fractional Bayes factor for model comparison (with discussion). Journal of the Royal Statistical Society Series B, 57, 99-138.
38. O'Hagan, A. and Forster, J. (2004). Bayesian Inference. Kendall's Advances Theory of Statistics (Vol. 2B). London: Arnold.
39. Pawitan, Y. (2001). In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press: Oxford.
40. San Martini, A. and Spezaferri, F. (1984). A predictive model selection criterion. Journal of the Royal Statistical Sociery, Series B, 46, 296-303.
41. Sellke, T., Bayarri, M.J. and Berger, J. (2001). Calibration of p-values for testing precise null hypotheses. The American Statistician, 55, 62-71.
42. Wald, A. (1955). Testing the difference between the means of two normal populations with unknown standard deviations. In Selected papers in Statistics and Probability, T.W. Anderson et al. (eds.), 669-695, Stanford University Press.
43. Wilks, S.S. (1962). Mathematical Statistics. New York: Wiley
44. Welch, B.L. (1951). On the comparison of several means values: an alternative approach. Biometrika, 38, 330-336.
45. Zellner, A. (1986). On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In Bayesian Inference and Decision Techniques: Essays in Honour of Bruno de Finetti, P.K. Goel and A. Zellner (eds.), 233-243, Amsterdam: Elsevier.