We introduce a novel and flexible framework for constructing locally adaptive 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, this framework -- which we call Gibbs self-tuning (GIST) -- encompasses randomized HMC, multinomial HMC, the No-U-Turn Sampler (NUTS), and the Apogee-to-Apogee Path Sampler as special cases. The GIST framework is illustrated with a novel alternative to NUTS for locally adapting path lengths, evaluated with an exact Hamiltonian for a high-dimensional, ill-conditioned Gaussian measure and with the leapfrog integrator for a suite of diverse models.

翻译：本文提出了一种新颖且灵活的框架，用于构建局部自适应哈密顿蒙特卡洛（HMC）采样器，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调整算法的超参数。在自适应采样路径长度方面，该框架——我们称之为吉布斯自调优（GIST）——将随机化HMC、多项HMC、无U形回转采样器（NUTS）以及远地点至远地点路径采样器均涵盖为特例。我们通过一种新颖的NUTS替代方案来阐释GIST框架在局部自适应路径长度中的应用，并分别采用精确哈密顿量对高维病态高斯测度、以及跳蛙积分器对一系列多样化模型进行了评估。