Work

Incorporating local step-size adaptivity into the no-U-turn sampler using Gibbs self-tuning

Year: 2025

Type: article

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.

Source: The Journal of Chemical Physics

DOI: 10.1063/5.0280793

Authors: Nawaf Bou-Rabee, Bob Carpenter, Tore Selland Kleppe, Milo Marsden

Institutions: Rutgers, The State University of New Jersey, Flatiron Institute, University of Stavanger, Stanford University

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Collaborative Research: Numerical Methods for High-Dimensional Sticky Diffusions