| Abstract: | When no information is available and hence improper noninformative priors should be used, Bayes factor includes the unspecified constants and can not be calibrated. To solve this problem, we modify the intrinsic Bayes factor (IBF) of Berger and Pericchi 1-2 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. Berger, J. O. and Pericchi, L. R. 1998. Accurate and Stable Bayesian Model Selection: The Median Intrinsic Bayes Factor. Sankhya, Series B, 60: 1–18. and the fractional Bayes factor (FBF) of O'Hagan 3] O'Hagan, A. 1995. Fractional Bayes Factors for Model Comparison. Journal of the Royal Statistical Society, Series B, 57: 99–138. Google Scholar] with the generalized Savage-Dickey density ratio of Verdinelli and Wasserman 4] Verdinelli, I. and Wasserman, L. 1995. Computing Bayes Factors Using a Generalization of Savage-Dickey Density Ratio. Journal of the American Statistical Association, 90: 614–618. Taylor & Francis Online], Web of Science ®] , Google Scholar]. These modified IBF and FBF are applied to detecting outliers in random effects models with a mean-shift structure. The proposed methodology is exemplified by a simulation experiment with a generated data set and also applied to a real data set, Dyestuff data in Box and Tiao 5] Box, G. E.P. and Tiao, G. C. 1973. Bayesian Inference in Statistical Analysis U.S.A.: Addison-Wesley Publishing Co.. Google Scholar] |
