Nonparametric Bayesian modelling using skewed Dirichlet processes

We introduce a new class of discrete random probability measures that extend the definition of Dirichlet process (DP) by explicitly incorporating skewness. The asymmetry is controlled by a single parameter in such a way that symmetric DPs are obtained as a special case of the general construction. We review the main properties of skewed DPs and develop appropriate Polya urn schemes. We illustrate the modelling in the context of linear regression models of the capital asset pricing model (CAPM) type, where assessing symmetry for the error distribution is important to check validity of the model.