Sampling inference, Bayes’ inference, and robustness in the advancement of learning

  • G. E. P. Box
Sensitivity to Models Invited Papers


Scientific learning is seen as an iterative process employing Criticism and Estimation. Sampling theory use of predictive distributions for model criticism is examined and also the implications for significance tests and the theory of precise measurement. Normal theory examples and ridge estimates are considered. Predictive checking functions for transformation, serial correlation, and bad values are reviewed as is their relation with Bayesian options. Robustness is seen from a Bayesian view point and examples are given The bad value problem is also considered and comparison withM estimators is made.


Iterative Learning Model Building Inference Bayes Pheorem Sampling Theory Predictive Distribution Diagnostics Checks Transformations Serial Correlation Bad Values Outliers Cobist Estimation 


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References in the Discussion

  1. BOX, G.E.P. and TIAO, G.C. (1962). A further look at robustness via Bayes’s theorem.Biometrika 49, 419–432.MATHMathSciNetGoogle Scholar
  2. GOOD, I.J. and GASKINS, R.A. (1980). Density estimation and bump-hunting by the penalized likelihood method exemplified by scatering and meteorite data.J. Amer. Statist. Assoc. 75, 42–73 (with discussion).MATHCrossRefMathSciNetGoogle Scholar
  3. O’HAGAN, A. (1979). On outlier rejection phenomena in Bayes inference.J. Roy. Statist. Soc. B. 41, 358–367.MATHMathSciNetGoogle Scholar

Copyright information

© Springer 1980

Authors and Affiliations

  • G. E. P. Box
    • 1
  1. 1.University of Wisconsin-MadisonMadisonUSA

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