Towards practical PDMP sampling: Metropolis adjustments, locally adaptive step-sizes, and NUTS-based time lengths
Abstract
Piecewise-Deterministic Markov Processes (PDMPs) hold significant promise for sampling from complex probability distributions. However, their practical implementation is hindered by the need to compute model-specific bounds. Conversely, while Hamiltonian Monte Carlo (HMC) offers a generally efficient approach to sampling, its inability to adaptively tune step sizes impedes its performance when sampling complex distributions like funnels. To address these limitations, we introduce three innovative concepts: (a) a Metropolis-adjusted approximation for PDMP simulation that eliminates the need for explicit bounds without compromising the invariant measure, (b) an adaptive step size mechanism compatible with the Metropolis correction, and (c) a No U-Turn Sampler (NUTS)-inspired scheme for dynamically selecting path lengths in PDMPs. These three ideas can be seamlessly integrated into a single, `doubly-adaptive' PDMP sampler with favourable robustness and efficiency properties.
Cite
@article{arxiv.2503.11479,
title = {Towards practical PDMP sampling: Metropolis adjustments, locally adaptive step-sizes, and NUTS-based time lengths},
author = {Augustin Chevallier and Sam Power and Matthew Sutton},
journal= {arXiv preprint arXiv:2503.11479},
year = {2025}
}