Bayesian inference for linear regression under alpha-skew-normal prior - Alhamide, A.A.; Kamarulzaman Ibrahim,; Alodat, M.T.; Wan Zawiah Wan Zin, (Penerbit Universiti Kebangsaan Malaysia, 2019)
A study on Bayesian inference for the linear regression model is carried out in the case when the prior distribution for the regression parameters is assumed to follow the alpha-skew-normal distribution. The posterior distribution and its associated full conditional distributions are derived. Then, the Bayesian point estimates and credible intervals for the regression parameters are determined based on a simulation study using the Markov chain Monte Carlo method. The parameter estimates and intervals obtained are compared with their counterparts when the prior distributions are assumed either normal or non-informative. In addition, the findings are applied to Scottish hills races data. It appears that when the data are skewed, the alpha-skew-normal prior contributes to a more precise estimate of the regression parameters as opposed to the other two priors.