Bayes Factors for Outlier Models Using the Device of Imaginary Observations

References

• Abraham , B. and Box , G. E. P. 1978 . Linear Models and Spurious Observations . Applied Statistics , 27 : 120 – 130 .
   Google Scholar
• Barnett , V. and Lewis , T. 1984 . Outliers in Statistical Data, , 2nd ed. , Chichester , , UK : John Wiley .
   Google Scholar
• Box , G. E. P. and Tiao , G. C. 1968 . A Bayesian Approach to Some Outlier Problems . Biometrika , 55 : 119 – 129 .
   PubMed Web of Science ®Google Scholar
• Cook , R. D. and Weisberg , S. 1982 . Residuals and Influence in Regression , New York : Chapman and Hall .
   Google Scholar
• Draper , N. R. and John , J. A. 1981 . Influential Observations and Outliers in Regression . Technometrics , 23 : 21 – 26 .
   Web of Science ®Google Scholar
• Fisher , R. A. 1960 . The Design of Experiments, , 7th ed. , New York : Hafner Press .
   Google Scholar
• Freeman , P. R. 1980 . “ On the Number of Outliers in Data From a Linear Model ” . In Bayesian Statistics , Edited by: Bernardo , J. M. , DeGroot , M. H. , Lindley , D. V. and Smith , A. F. M. 349 – 365 . Valencia , , Spain : Valencia University Press . (with discussion)
   Google Scholar
• Guttman , I. , Dutter , R. and Freeman , P. R. 1978 . Care and Handling of Univariate Outliers in the General Linear Model to Detect Spuriosity–A Bayesian Approach . Technometrics , 20 : 187 – 193 .
   Web of Science ®Google Scholar
• Guttman , I. and Peña , D. 1988 . “ Outliers and Influence: Evaluation by Posteriors of Parameters in the Linear Model ” . In Bayesian Statistics 3 , Edited by: Bernardo , J. M. , DeGroot , M. H. , Lindley , D. V. and Smith , A. F. M. 631 – 640 . Oxford , , UK : Oxford University Press .
   Google Scholar
• Jeffreys , H. 1961 . Theory of Probability , Oxford , , UK : Oxford University Press .
   Google Scholar
• Kimber , A. C. 1982 . Tests for Many Outliers in an Exponential Sample . Applied Statistics , 31 : 263 – 271 .
   Web of Science ®Google Scholar
• Kimber , A. C. and Stevens , H. J. 1981 . The Null Distribution of a Test for Two Upper Outliers in an Exponential Sample . Applied Statistics , 30 : 153 – 157 .
   Google Scholar
• Mickey , M. R. , Dunn , O. J. and Clark , V. 1967 . Note on the Use of Stepwise Regression in Detecting Outliers . Computers and Biomedical Research , 1 : 105 – 111 .
   PubMedGoogle Scholar
• Peña , D. and Tiao , G. C. 1992 . “ Bayesian Robust Functions for Linear Models ” . In Bayesian Statistics 4 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. Oxford , , UK : Oxford University Press . Proceedings of the Fourth Valencia International Meeting on Bayesian Statistics
   Google Scholar
• Pettit , L. I. 1988 . Bayes Methods for Outliers in Exponential Samples . Journal of the Royal Statistical Society , 50 : 371 – 380 . Ser. B
   Google Scholar
• Pettit , L. I. and Smith , A. F. M. 1983 . Bayesian Model Comparison in the Presence of Outliers . Bulletin of the International Statistical Institute , 50 : 292 – 309 .
   Google Scholar
• Pettit , L. I. and Smith , A. F. M. 1985 . “ Outliers and Influential Observations in Linear Models ” . In Bayesian Statistics 2 , Edited by: Bernardo , J. M. , DeGroot , M. H. , Lindley , D. V. and Smith , A. F. M. 473 – 494 . Amsterdam : North-Holland . (with discussion)
   Google Scholar
• Smith , A. F. M. and Spiegelhalter , D. J. 1981 . “ Bayesian Approaches to Multivariate Structure ” . In Interpreting Multivariate Data , Edited by: Barnett , V. 335 – 348 . Chichester , , UK : John Wiley .
   Google Scholar
• Spiegelhalter , D. J. and Smith , A. F. M. 1982 . Bayes Factors for Linear and Log-Linear Models With Vague Prior Information . Journal of the Royal Statistical Society , 44 : 377 – 387 . Ser. B
   Google Scholar