Bayesian inference for linear regression under alpha-skew-normal prior

• Main Authors: Alhamide, A.A., Kamarulzaman Ibrahim,, Alodat, M.T., Wan Zawiah Wan Zin,
• Format: Article
• Language: English
• Published: Penerbit Universiti Kebangsaan Malaysia 2019
• Online Access: http://journalarticle.ukm.my/13072/1/26%20Alhamide%2C%20A.A.pdf; http://journalarticle.ukm.my/13072/; http://www.ukm.my/jsm/malay_journals/jilid48bil1_2019/KandunganJilid48Bil1_2019.html

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.