Bayesian Unmasking in Linear Models

We propose a Bayesian procedure for multiple outlier detection in linear models avoiding the masking problem. Our proposal is illustrated with several examples in which our procedure outperforms other recent methods for multiple outlier detection. The posterior probabilities of each data point being an outlier are estimated by using a new adaptive Gibbs sampling method, which modifies the initial conditions of the Gibbs sampler by using the eigenstructure of the covariance matrix of the indicator variables. This procedure also overcomes the false convergence of the Gibbs sampling in problems with strong masking.