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A ROBUST BAYES FACTOR FOR LINEAR MODELS
Author(s) -
Taplin Ross H.
Publication year - 2005
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2005.00408.x
Subject(s) - bayes factor , outlier , bayes' theorem , variance inflation factor , mathematics , bayes' rule , statistics , bayes error rate , robustness (evolution) , robust statistics , bayes classifier , artificial intelligence , computer science , bayesian probability , linear regression , multicollinearity , biochemistry , chemistry , gene
Summary This paper proposes a new robust Bayes factor for comparing two linear models. The factor is based on a pseudo‐model for outliers and is more robust to outliers than the Bayes factor based on the variance‐inflation model for outliers. If an observation is considered an outlier for both models this new robust Bayes factor equals the Bayes factor calculated after removing the outlier. If an observation is considered an outlier for one model but not the other then this new robust Bayes factor equals the Bayes factor calculated without the observation, but a penalty is applied to the model considering the observation as an outlier. For moderate outliers where the variance‐inflation model is suitable, the two Bayes factors are similar. The new Bayes factor uses a single robustness parameter to describe a priori belief in the likelihood of outliers. Real and synthetic data illustrate the properties of the new robust Bayes factor and highlight the inferior properties of Bayes factors based on the variance‐inflation model for outliers.