This paper introduces Prior Knowledge Acceleration (PKA), a method to speed up variance calculations by leveraging prior knowledge of the original dataset's variance. PKA enables the efficient updating of variance when adding new data, reducing computational costs by avoiding full recalculations. We derive expressions for both population and sample variance using PKA and compare it to Sheldon M. Ross's method. Stimulated results show that PKA can reduce calculation time by up to 75.6%, especially when the original dataset is large. PKA offers a promising approach for accelerating variance computations in large-scale data analysis, though its effectiveness depends on assumptions of constant computational time.

翻译：本文提出了一种名为先验知识加速（PKA）的方法，该方法通过利用原始数据集方差的先验知识来加速方差计算。PKA能够在添加新数据时高效更新方差，通过避免完全重新计算来降低计算成本。我们推导了使用PKA的总体方差和样本方差的表达式，并将其与Sheldon M. Ross的方法进行了比较。模拟结果表明，PKA可以将计算时间减少高达75.6%，尤其是在原始数据集规模较大时。PKA为大规模数据分析中的方差计算加速提供了一种有前景的途径，尽管其有效性依赖于计算时间恒定的假设。