NUTS for NUTS: New Advances in No-U-Turn SamplersColloquium CRC 1720

by Nawaf Bou-Rabee

Tuesday Jun 9, 2026, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Markov chain Monte Carlo (MCMC) remains a central tool for sampling from intractable distributions, yet the efficiency of classical algorithms often deteriorates in high dimensions or anisotropic geometries. The No-U-Turn Sampler (NUTS) and its descendants have transformed practical Bayesian computation by adapting trajectory lengths to local geometry, enabling efficient exploration even in complex, high-dimensional landscapes.  Despite their empirical success, a rigorous understanding of why such locally adaptive schemes mix efficiently has remained elusive.

This talk revisits the mathematical foundations of NUTS and shows how they can be extended and unified within a broader framework. This perspective leads to new algorithms that preserve the self-tuning spirit of NUTS while extending its reach to ill-conditioned geometries.  Along the way, we will see how No-U-Turn ideas are evolving from clever computational innovations into a principled theory of locally adaptive MCMC, bringing us closer to the long-standing program of constructing samplers that require no tuning with provable efficiency guarantees.