Bayesian Analysis of Skew Normal Mixture Regression

Regression analysis is done, traditionally, considering homogeneity and normality assumption for the response variable distribution. Whereas in many applications, observations indicate to a heterogeneous structure containing some sub-populations with skew-symmetric structure either due to heterogeneity, multimodality or skewness of the population or a combination of them. In this situations, one can use a mixture of skew-symmetric distributions to model the population. In this paper we considered the Bayesian approach of regression analysis under the assumption of heterogeneity of population and a skew-symmetric distribution for sub-populations, by using a mixture of skew normal distributions. We used a simulation study and a real world example to assess the proposed Bayesian methodology and to compare it with frequentist approach.