Bayesian unmasking in linear models
We propose a Bayesian procedure for multiple outlier detection in linear models which avoids the masking problem. The posterior probabilities of each data point being an outlier are estimated by using an adaptive learning Gibbs sampling method. The idea is to modify the initial conditions of the Gibbs sampler in order to visit the posterior distribution space in a reasonable number of iterations. To find an appropriate vector of initial values we consider the information extracted from the eigenstructure of the covariance matrix of a vector of latent variables. These variables are introduced in the model to capture the heterogeneity in the data. This procedure also overcomes the false convergence of the Gibbs sampling in problems with strong masking. Our proposal is illustrated with some of the examples most frequently used in the literature.
multiple outliers gibbs sampler linear regression sequential learning