Sub-Cauchy Sampling: Escaping the Dark Side of the Moon

Sebastiano Grazzi; Sifan Liu; Gareth O. Roberts; Jun Yang

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arXiv · 2601.11066

Sub-Cauchy Sampling: Escaping the Dark Side of the Moon

Sebastiano Grazzi·Sifan Liu·Gareth O. Roberts·Jun Yang

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Abstract

We introduce a Markov chain Monte Carlo algorithm based on Sub-Cauchy Projection, a geometric transformation that generalizes stereographic projection by mapping Euclidean space into a spherical cap of a hyper-sphere, referred to as the complement of the dark side of the moon. We prove that our proposed method is uniformly ergodic for sub-Cauchy targets, namely targets whose tails are at most as heavy as a multidimensional Cauchy distribution, and show empirically its performance for challenging high-dimensional problems. The simplicity and broad applicability of our approach open new opportunities for Bayesian modeling and computation with heavy-tailed distributions in settings where most existing methods are unreliable.

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Sebastiano Grazzi, Sifan Liu, Gareth O. Roberts, Jun Yang. 2026-01-16. Sub-Cauchy Sampling: Escaping the Dark Side of the Moon. https://arxiv.org/abs/2601.11066

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