In this paper, we derived the posterior density function of parameters of linear regression model when the various structures of heteroscedasticity consistent covariance estimators developed by White (1980) Mackinnon and White (1985) and and Cribari-Neto (2004) were incorporated. We specify non-informative uniform prior for the parameters of the model . From the joint posterior density function, we derived the marginal density of via Gibbs Sampler. The marginal density of follows normal and Wishart distribution respectively. For the Bayes estimator, the Gibbs Sampler was utilized to obtain random draws of the parameters. As indicated in similar research in the past where the OLS estimator was used as estimate, the Bayes estimator is more robust and reliable for inference problem for small and large sample sizes.
Keywords: Heteroscedasticity, Posterior, Bayesian, Gibbs sampling, Noninformative prior.