Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions in highdimensional spaces, the efficiency of importance sampling critically depends on the choice of the proposal distribution. In this paper, we propose a novel adaptive scheme for the construction of efficient proposal distributions. Our algorithm promotes efficient exploration of the target distribution by combining global sampling mechanisms with a delayed weighting procedure. The proposed weighting mechanism plays a key role by enabling rapid resampling in regions where the proposal distribution is poorly adapted to the target. Our sampling algorithm is shown to be geometrically convergent under mild assumptions and is illustrated through various numerical experiments.

翻译：重要性采样是一种蒙特卡洛方法，它通过从建议分布中抽取加权样本来构建目标分布期望的估计量。当目标分布较为复杂时，例如高维空间中的多峰分布，重要性采样的效率关键取决于建议分布的选择。本文提出了一种构建高效建议分布的新型自适应方案。我们的算法通过将全局采样机制与延迟加权过程相结合，促进对目标分布的有效探索。所提出的加权机制在建议分布与目标分布适配较差的区域能够实现快速重采样，从而发挥关键作用。在温和假设下，我们的采样算法被证明具有几何收敛性，并通过多种数值实验进行了验证。