Nonparametric Bayesian Modelling Using Skewed Dirichlet Processes Pilar Iglesias Z., Yasna Orellana Z. and Fernando A. Quintana ∗ July 30, 2008 Abstract 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 CAPM type, where assessing symmetry for the error distribution is important to check validity of the model. Key Words: Bayes Factor, Density Estimation, Dirichlet Process, Linear Regres- sion Model, Polya Sequence, Skewed Distribution. * Departamento de Estad´ ıstica, Facultad de Matem´ aticas, PontificiaUniversidad Cat´olicade Chile, Casilla 306, Correo 22, Santiago, CHILE. Contact e-mail: quintana@mat.puc.cl. This article is dedi- cated to the memory of Pilar L. Iglesias, a friend who is still very much missed. 1