<p>The linear prediction evolution algorithm (LPE) has recently emerged in the area of optimization algorithms. It is characterized by its simplicity, as it utilizes only a few parameters, while still possessing a high exploration capability. Although ILPE has demonstrated promising results in solving CEC 2014 and CEC 2017 benchmark problems, it is not without limitations, such as its slow convergence speed and the solution quality. To address these limitations and further enhance the exploration capability of the ILPE algorithm, this study introduces a modified version called the Bayesian estimation based improved linear prediction evolution algorithm (BILPE). The BILPE algorithm approaches the population series of evolutionary algorithms as a time series and incorporates nonlinear least square fitting technique, a probability calculated by Bayesian estimation, and a directional guidance mechanism as a reproduction operator to predict the offsprings of the next generation. To evaluate the effectiveness of the proposed algorithm, it is tested on the CEC 2014, CEC 2017, and CEC 2022 benchmark functions, as well as four engineering design problems, which are commonly used in optimization research. The results of the comparison between BILPE and ILPE demonstrate that BILPE outperforms its predecessor in terms of solution quality and convergence speed. Furthermore, BILPE exhibits competitive performance when compared to other state-of-the-art optimization algorithm.</p>