Monte Carlo integration is fundamental in scientific and statistical computation, but requires reliable samples from the target distribution, which poses a substantial challenge in the case of multi-modal distributions. Existing methods often involve time-consuming tuning, and typically lack tailored estimators for efficient use of the samples. This paper adapts the Warp-U transformation [Wang et al., 2022] to form multi-modal sampling strategy called Warp-U sampling. It constructs a stochastic map to transport a multi-modal density into a uni-modal one, and subsequently inverts the transport but with new stochasticity injected. For efficient use of the samples for normalising constant estimation, we propose (i) an unbiased estimation scheme based coupled chains, where the Warp-U sampling is used to reduce the coupling time; and (ii) a stochastic Warp-U bridge sampling estimator, which improves its deterministic counterpart given in Wang et al. [2022]. Our overall approach requires less tuning and is easier to apply than common alternatives. Theoretically, we establish the ergodicity of our sampling algorithm and that our stochastic Warp-U bridge sampling estimator has greater (asymptotic) precision per CPU second compared to the Warp-U bridge estimator of Wang et al. [2022] under practical conditions. The advantages and current limitations of our approach are demonstrated through simulation studies and an application to exoplanet detection.

翻译：蒙特卡洛积分是科学与统计计算的基础，但需要从目标分布中获取可靠样本，这在多模态分布情况下构成重大挑战。现有方法往往需要耗时调参，且通常缺乏针对样本高效利用的定制化估计器。本文对Warp-U变换[Wang et al., 2022]进行改进，形成名为Warp-U采样的多模态采样策略。该方法构建随机映射将多模态密度输运为单模态密度，随后通过注入新的随机性来反转该输运过程。为高效利用样本进行归一化常数估计，我们提出：(i) 基于耦合链的无偏估计方案，利用Warp-U采样缩短耦合时间；(ii) 随机Warp-U桥采样估计器，该估计器优于Wang et al. [2022]中给出的确定性对应方法。整体方法所需的调参量少于常见替代方案且更易应用。理论上，我们证明了采样算法的遍历性，并论证在实际条件下，所提出的随机Warp-U桥采样估计器相较于Wang et al. [2022]的Warp-U桥估计器具有更高的（渐近）每CPU秒精度。通过仿真研究及系外行星探测应用案例，展示了本方法的优势与当前局限性。