Bayesian Sensitivity Analysis and Model Comparison for Skew Elliptical Models I. Vidal a,*,1 , P. Iglesias b,2 , M. D. Branco c and R. B. Arellano-Valle b,3 a Instituto de Matem´ atica y F´ ısica, Universidad de Talca, Casilla 721, Chile b Pontificia Universidad Cat´ olica de Chile c Universidade de S˜ ao Paulo, Brazil Abstract In this work we approach the problem of model comparison between skew fam- ilies. For the univariate skew model, we measure the sensitivity of the skewness parameter using the L 1 -distance between symmetric and asymmetric models and we obtain explicit expressions for some of these models. The main result is that the L 1 -distance between a representable elliptical distribution and a representable skew elliptical distribution remains invariant and it equals to the L 1 -distance between the normal and skew normal densities. We also use the Bayes factor to test asymmetry and present some simulation results for the skew-normal and skew-t distributions obtaining expected results for adequate prior distribution. An application in stock markets is also considered. Key words: Skew distribution, skew-normal distribution, representable skew elliptical distribution, Bayes factor, L 1 -distance. AMS subject classification number: 62F15 and 62F03. Short running title: Bayesian Sensitivity Analysis and Model Comparison. * Corresponding author. Tel.: 56-71-200313; fax: 56-71-200392 Email address: ividal@inst-mat.utalca.cl (I. Vidal). 1 This work has been supported by grant DIAT, Universidad de Talca. 2 Partially supported by grant FONDECYT-1030588. 3 Partially supported by grant FONDECYT-1040865. Preprint submitted to J. Statist. Planning and Inference 17 November 2004