A method for simultaneous variable selection and outlier identification in linear regression*

We suggest a method for simultaneous variable selection and outlier identification based on the computation of posterior model probabilities. This avoids the problem that the model you select depends upon the order in which variable selection and outlier identification are carried out. Our method can find multiple outliers and appears to be successful in identifying masked outliers. We also address the problem of model uncertainty via Bayesian model averaging. For problems where the number of models is large, we suggest a Markov chain Monte Carlo approach to approximate the Bayesian model average over the space of all possible variables and outliers under consideration. Software for implementing this approach is described. In an example, we show that model averaging via simultaneous variable selection and outlier identification improves predictive performance and provides more accurate prediction intervals as compared to any single model that might reasonably be selected. Keywords" Bayesian model averaging; Markov chain Monte Carlo model composition; Masking; Model uncertainty; Posterior model probability