Computational Mathematics and Scientific Computing Seminar

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Many MCMC methods either rely on gradients (e.g., NUTS) or struggle with multi-scale distributions, where different regions require vastly different exploration strategies.  The No-Underrun Sampler (NURS) is a new gradient-free, locally adaptive MCMC method that combines ideas from Hit-and-Run and NUTS while remaining simple to implement and inherently parallelizable. NURS selects random update directions uniformly from the unit sphere and introduces an adaptive orbit-based exploration that adjusts to the local scale of the target distribution.

Empirical results on Neal’s funnel, a challenging multi-scale benchmark, show that while NURS moves diffusively in narrow regions, it transitions to ballistic movement in broader ones, enabling efficient sampling across the distribution’s different scales. I will also discuss NURS’s formal connections to Hit-and-Run, quantitative tuning guidelines, and new coupling results. By offering a locally adaptive, theoretically grounded approach for sampling multi-scale distributions, NURS broadens the scope of gradient-free MCMC – an area that remains surprisingly underexplored. 

For details, see the companion paper: https://arxiv.org/abs/2501.18548