Modeling the Nature and Frequency of Outliers.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Bayesian techniques are applied to the problem of dealing with the possible occurrence of outlying observations. Since most experimental data are liable to occasional discrepancies, a robustification approach is taken whereby this experimental fact of life is taken into account in the model. Special consideration is given to the way in which both the nature and the frequency of the outlying observations are modeled. In this regard, the Bayesian outlier procedure of Box and Tiao, which assumes a contaminated error distribution with alpha denoting the frequency of contamination, is developed further. In particular, alpha is not assumed to be known, but rather, a prior distribution is used to express uncertainty about its value. When combined with the information about alpha contained in the data itself, it is seen that appropriate inferences about this outlier frequency can be made. A detailed example is presented. Author
- Statistics and Probability