The local pivotal method (LPM) is a successful sampling method for taking well-spread samples from discrete populations. We show how the LPM can be utilized to sample from arbitrary continuous distributions and thereby give powerful variance reduction in general cases. The method creates an ``automatic stratification" on any continuous distribution, of any dimension, and selects a ``thin" well-spread sample. We demonstrate the simplicity, generality and effectiveness of the LPM with various examples, including Monte Carlo estimation of integrals, option pricing and stability estimation in non-linear dynamical systems. Additionally, we show how the LPM can be combined with other variance reduction techniques, such as importance sampling, to achieve even greater variance reduction. To facilitate the implementation of the LPM, we provide a quick start guide to using LPM in MATLAB and R, which includes sample code demonstrating how to achieve variance reduction with just a few lines of code.

翻译：局部支点方法（LPM）是一种从离散总体中获取均匀分布样本的成功采样方法。我们展示了如何利用LPM从任意连续分布中采样，从而在一般情况下实现强大的方差缩减。该方法可在任意维度的连续分布上创建"自动分层"，并选取"薄"且均匀分布的样本。通过多个实例（包括蒙特卡洛积分估计、期权定价以及非线性动力系统稳定性估计）论证了LPM的简洁性、通用性和有效性。此外，我们展示了如何将LPM与其他方差缩减技术（如重要性采样）结合，以实现更大幅度的方差缩减。为便于LPM实施，我们提供了在MATLAB和R中使用LPM的快速入门指南，其中包含仅需数行代码即可实现方差缩减的示例代码。