In this work, we introduce the No-Underrun Sampler (NURS), a locally-adaptive, gradient-free Markov chain Monte Carlo method that blends ideas from Hit-and-Run and the No-U-Turn Sampler. NURS dynamically adapts to the local scale of the target distribution without requiring gradient evaluations, making it especially suitable for applications where gradients are unavailable or costly. We establish key theoretical properties, including reversibility, formal connections to Hit-and-Run and Random Walk Metropolis, Wasserstein contraction comparable to Hit-and-Run in Gaussian targets, and bounds on the total variation distance between the transition kernels of Hit-and-Run and NURS. Empirical experiments, supported by theoretical insights, illustrate the ability of NURS to sample from Neal's funnel, a challenging multi-scale distribution from Bayesian hierarchical inference.

翻译：本文提出无欠采样器（NURS），这是一种融合了命中-逃逸采样器与无U形转向采样器思想的局部自适应、无梯度马尔可夫链蒙特卡洛方法。NURS能够动态适应目标分布的局部尺度，且无需梯度计算，使其特别适用于梯度不可得或计算成本高昂的应用场景。我们建立了关键的理论性质，包括可逆性、与命中-逃逸采样器及随机游走Metropolis算法的形式化关联、在高斯目标分布中与命中-逃逸采样器相当的Wasserstein收缩性，以及命中-逃逸采样器与NURS转移核之间总变差距离的界。基于理论洞见的实证实验表明，NURS能够有效对Neal漏斗分布（贝叶斯层次推断中一个具有挑战性的多尺度分布）进行采样。