This chapter discusses methods that allow taking into account a priori information in estimation problems. The main attention is paid to estimating the parameters of linear regression, since estimating the mathematical expectation is a special case of this problem. The essence of the Bayesian method is considered as applied to estimating linear regression parameters and its random component variance under various assumptions. The features of the method and the possibility of its transformation are discussed. In this regard, various methods of unbiased and biased estimation are discussed, which allow increasing the accuracy of estimation. These methods also allow to increase the regression forecast accuracy. Methods for estimating variable regression parameters are also considered here. Among them, the methods for constructing switching regressions with unknown switching points stand out.