Incorporating Local Step-Size Adaptivity into the No-U-Turn Sampler using Gibbs Self Tuning
Abstract
Adapting the step size locally in the no-U-turn sampler (NUTS) is challenging because the step-size and path-length tuning parameters are interdependent. The determination of an optimal path length requires a predefined step size, while the ideal step size must account for errors along the selected path. Ensuring reversibility further complicates this tuning problem. In this paper, we present a method for locally adapting the step size in NUTS that is an instance of the Gibbs self-tuning (GIST) framework. Our approach guarantees reversibility with an acceptance probability that depends exclusively on the conditional distribution of the step size. We validate our step-size-adaptive NUTS method on Neal's funnel density and a high-dimensional normal distribution, demonstrating its effectiveness in challenging scenarios.
Cite
@article{arxiv.2408.08259,
title = {Incorporating Local Step-Size Adaptivity into the No-U-Turn Sampler using Gibbs Self Tuning},
author = {Nawaf Bou-Rabee and Bob Carpenter and Tore Selland Kleppe and Milo Marsden},
journal= {arXiv preprint arXiv:2408.08259},
year = {2025}
}
Comments
for companion code, see https://github.com/bob-carpenter/adaptive-hmc