In the general linear regression model, the use of stochastic smoothness prior knowledge has been encountered as an important analysis technique in recent years for estimating the parameters. The way to apply this method in the most effective and most meaningful way is possible by using the Bayesian approach. The feature that reflects the characteristic of Bayesian regression analysis is that prior knowledge is included in the analysis. In the Bayesian approach, prior knowledge of the parameter is included in the analysis before the trials are performed, due to the preliminary probability density function. In this study, theoretical implications that can be used in case of stochastic prior knowledge to estimate parameters in Bayesian regression model are discussed.