Bayesian model selection approach to analysis of variance under heteroscedasticity

Journal of the Royal Statistical Society Series D: The Statistician

Volumn 49, Issue 4, 2000, Pages 495-502

  Bertolino, Francesco ^a   Racugno, Walter ^a   Moreno, Elías ^a  

^a UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

Bayes factors; Default bayesian analysis of variance; Fractional priors; Heteroscedasticity; Intrinsic priors

Indexed keywords

EID: 0039335091     PISSN: 00390526     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9884.00249     Document Type: Article

References (23)

1. Berger, J. and Mortera, J. (1995) Discussion on 'Fractional Bayes factors for model comparison' (by A. O'Hagan). J. R. Statist. Soc. B, 57, 130-131.
2. Berger, J. O. and Pericchi, L. R. (1996a) The intrinsic Bayes factor for model selection and prediction. J. Am. Statist. Ass., 91, 109-122.
3. _(1996b) On the justification of default and intrinsic Bayes factor. In Modelling and Prediction (eds J. C. Lee et al.), pp. 276-293. New York: Springer.
4. _(1997) On criticism and comparison of default Bayes factors for model selection and hypothesis testing. In Proc. Wrkshp Model Selection (ed. W. Racugno), pp. 1-50. Bologna: Pitagora.
5. Box, G. E. P. and Tiao, G. C. (1973) Bayesian Inference in Statistical Analysis. Reading: Addison-Wesley.
6. Brown, M. B. and Forsythe, A. B. (1974a) The ANOVA and multiple comparisons for data with heterogeneous variances. Biometrics, 30, 719-724.
7. _(1974b) The small sample behaviour of some statistics which test the equality of several means. Technometrics, 16, 129-132.
8. De Santis, F. and Spezzaferri, F. (1999) Methods for default and robust Bayesian model comparison: the fractional Bayes factor approach. Int. Statist. Rev., 67, 267-286.
9. Jeffreys, H. (1961) Theory of Probability. London: Oxford University Press.
10. Kass, R. E. and Wasserman, L. (1985) A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. J. Am. Statist. Ass., 90, 928-934.
11. _(1996) The selection of prior distributions by formal rules. J. Am. Statist. Ass., 91, 1343-1370.
12. Lindley, D. V. (1970) An Introduction to Probability and Statistics from a Bayesian Viewpoint, vol. 2. Cambridge: Cambridge University Press.
13. Moreno, E. (1997) Bayes factor for intrinsic and fractional priors in nested models: Bayesian robustness. IMS Lect. Notes, 31, 257-270.
14. Moreno, E., Bertolino, F. and Racugno, W. (1998) An intrinsic limiting procedure for model selection and hyphotheses testing. J. Am. Statist. Ass., 93, 1451-1460.
15. O'Hagan, A. (1994) Bayesian Inference: Kendall's Advanced Theory of Statistics, vol. 2B. London: Arnold.
16. _(1995) Fractional Bayes factors for model comparison (with discussion). J. R. Statist. Soc. B, 57, 99-138.
17. _(1997) Properties of intrinsic and fractional Bayes factors. Test, 1, 101-118.
18. Scheffé, H. (1959) The Analysis of Variance. New York: Wiley.
19. Schwarz, G. (1978) Estimating the dimension of a model. Ann. Statist., 6, 461-464.
20. Stuart, A. and Ord. J. K. (1991) Classical Inference and Relationship: Kendall's Advanced Theory of Statistics, vol. 2. London: Arnold.
21. Tan, W. Y. and Tabatabai, M. A. (1986) Some Montecarlo studies on the comparison of several means under heteroscedasticity and robustness with respect to departure of normality. Biomed. J., 28, 801-814.
22. Welch, B. L. (1951) On the comparison of several means values: an alternative approach. Biometrika, 38, 330-336.
23. Wolfram, S. (1996) The Mathematica Book, 3rd edn. Cambridge: Cambridge University Press.