Properties of bayes factors based on test statistics

Scandinavian Journal of Statistics

Volumn 35, Issue 2, 2008, Pages 354-368

  Johnson, Valen E ^a,b  

^a UNIVERSITY OF TEXAS MD ANDERSON CANCER CENTER   (United States)

^b UNIVERSITY OF TEXAS   (United States)

Author keywords

AIC; Bayesian hypothesis test; Bayesian information criterion; Deviance statistic; EBIC; Likelihood ratio statistic; Marginal likelihood; Posterior model probability

Indexed keywords

EID: 43749095435     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2007.00576.x     Document Type: Article

References (30)

1. Aitkin, M. (1991). Posterior Bayes factors (with discussion). J. Roy. Statist. Soc. Ser. B 53, 111–128.
2. Albert, J. H. (1990). A Bayesian test for a two‐way contingency table using independence priors. Canad. J. Statist. 18, 347–363.
3. Berger, J. O. & Mortera, J. (1999). Default Bayes factors for nonnested hypothesis testing. J. Amer. Statist. Assoc. 94, 542–554.
4. Berger, J. O. & Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 91, 109–122.
5. Berger, J. O. & Pericchi, L. R. (1998). Accurate and stable Bayesian model selection: the median intrinsic Bayes factor. Sankhya Ser. B 60, 1–18.
6. Berger, J. O., Pericchi, L. R. & Varshavsky, J. A. (1998). Bayes factors and marginal distributions in invariant situations. Sankhya Ser. A 60, 307–321.
7. Billingsley, P. (1986). Probability and measure. John Wiley & Sons, New York.
8. Cramér, H. (1946). Mathematical methods of statistics. Princeton University Press, Princeton, NJ.
9. Davidson, R. R. & Lever, W. E. (1970). The limiting distribution of the likelihood ratio statistic under a class of local alternatives. Sankhya Ser A 32, 209–224.
10. George, E. I. & McCulloch, R. E. (1993). Variable selection via Gibbs sampling. J. Amer. Statist. Assoc. 88, 881–889.
11. Hu, J. & Johnson, V. E. (2006). Bayesian model selection using test statistics. http://www.bepress.com/mdandersonbiostat/paper8/.
12. Jeffreys, H. (1935). Some tests of significance, treated by the theory of probability. Proc. Camb. Philos. Soc. 31, 201–222.
13. Jeffreys, H. (1961). Theory of probability. Oxford University Press, London.
14. Johnson, V. E. (2005). Bayes factors based on test statistics. J. Roy. Statist. Soc. Ser. B Stat. Methodol. 67, 689–701.
15. Kass, R. E. & Raftery, A. E. (1995). Bayes factors. J. Amer. Statist. Assoc. 90, 773–795.
16. Kass, R. E. & Wasserman, L. (1985). A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. J. Amer. Statist. Assoc. 90, 928–934.
17. Madigan, D. & Raftery, A. E. (1994). Model selection and accounting for model uncertainty in graphical models using Occam's window. J. Amer. Statist. Assoc. 89, 1535–1546.
18. McCulloch, R. E. & Rossi, P. E. (1993). Bayes factors for nonlinear hypotheses and likelihood distributions. Biometrika 79, 663–676.
19. Mitchell, J. J. & Beauchamp, J. J. (1988). Bayesian variable selection in linear regression (with discussion). J. Amer. Statist. Assoc. 83, 1023–1036.
20. O'Hagan, A. (1995). Fractional Bayes factors for model comparisons. J. Roy. Statist. Soc. Ser. B 57, 99–138.
21. Poirier, D. J. (1985). Bayesian hypothesis testing in linear models with continuously induced conjugate priors across hypotheses. In Bayesian statistics 2 (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley & A. F. M. Smith), 711–722. Elsevier, New York.
22. Randles, R. H. & Wolfe, D. A. (1979). Introduction to the theory of non‐parametric statistics. John Wiley & Sons, New York.
23. Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist. 6, 461–464.
24. Smith, A. F. M. & Spiegelhalter, D. J. (1980). Bayes factors and choice criteria for linear models. J. Roy. Statist. Soc. Ser. B 42, 213–220.
25. Spiegelhalter, D. J. & Smith, A. F. M. (1982). Bayes factors for linear and log‐linear models with vague prior information. J. Roy. Statist. Soc. Ser. B 44, 377–387.
26. Stewart, L. (1987). Hierarchical Bayesian analysis using Monte Carlo integration: computing posterior distributions when there are many possible models. Statistician 36, 211–219.
27. Verdinelli, I. & Wasserman, L. (1991). Bayesian analysis of outlier problems using the Gibbs Sampler. Stat. Comput. 1, 105–117.
28. Weakliem, D. L. (1999). A critique of the Bayesian information criterion for model selection. Sociol. Methods Res. 27, 359–397.
29. White, C. & Eisenberg, H. (1959). ABO blood groups and cancer of the stomach. Yale J. Biol. Med. 32, 58–61.
30. Zellner, A. & Siow, A. (1980). Posterior odds ratio for selected regression hypotheses. In Bayesian statistics. Proc. 1st int. meeting (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley & A. F. M. Smith), 585–603. University Press, Valencia.