Research on the Asymptotic Convergence of Bayesian Regression and Least Squares Regression under the Condition of Large Samples

Abstract

This paper compares the large-sample asymptotic convergence of Bayesian linear regression and ordinary least squares regression. It analyzes their fundamental differences from three aspects: theoretical foundations, convergence paths, and asymptotic performance, and points out the advantages of Bayesian methods in scenarios with moderate sample sizes and reliable prior information. Furthermore, a unified framework is constructed to reveal the relative efficiency of both methods under different model settings through mathematical derivation and simulation studies. Based on the Bernstein-von Mises theorem and asymptotic statistical theory, it is demonstrated that the two methods are asymptotically equivalent under regularity conditions. This provides a theoretical basis for method selection in practical applications.