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Incorporating Local Step-Size Adaptivity into the No-U-Turn Sampler using Gibbs Self Tuning
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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.
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Cited by 1 Pith paper
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On Accelerated Mixing of the No-U-turn Sampler
In Gaussian targets, NUTS is shown to select critical orbit lengths (and hence mix in O(1) transitions) exactly in a parameter phase A, while outside A there are step sizes for which it selects short orbits and mixes ...
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