Bayesian inference for the skewness parameter of the scalar skew-normal distribution

The skew-normal distribution includes the normal distribution as a special case. This family of distributions has a shape parameter that denes the direction of the asymmetry of the distribution, also called skewness parameter. The main focus of this paper will be showing that the Bayesian approach using MCMC methods is a good alternative to make inference under the skewness parameter. We present a brief discuss about prior choice and propose an approximation for the Jereys prior developed by Liseo and Loperdo (2006). We also provide an approximation for the bias correction factor proposed by Sartori (2006). A simulation study is presented to compare the bias, mean square error and interval estimates using the maximum likelihood and dierent Bayes estimators. Finally, hypotheses