We present a novel and flexible framework for localized tuning of Hamiltonian Monte Carlo (HMC) samplers by Gibbs sampling the algorithm's tuning parameters conditionally based on the position and momentum at each step. For adaptively sampling path lengths, the framework encompasses randomized HMC, multinomial HMC, the No-U-Turn Sampler (NUTS), and the Apogee-to-Apogee Path Sampler as special cases. The Gibbs self-tuning (GIST) framework is illustrated with an alternative to NUTS for locally adapting path lengths, evaluated with an exact Hamiltonian for an ill-conditioned normal and with the leapfrog algorithm for a test suite of diverse models.

翻译：我们提出了一种新颖且灵活的框架，用于对哈密顿蒙特卡洛（HMC）采样器进行局部调优，其方法是通过吉布斯采样，根据每一步的位置和动量条件性地采样算法的调优参数。对于自适应采样路径长度，该框架涵盖了随机化HMC、多项HMC、无U形转弯采样器（NUTS）以及远地点到远地点路径采样器作为特例。本文通过一个用于局部自适应路径长度的NUTS替代方案来阐述吉布斯自调优（GIST）框架，并使用一个病态正态分布的精确哈密顿量以及针对一系列多样化模型的蛙跳算法进行评估。