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Bibliographic Details
Main Authors: Grazzi, Sebastiano, Liu, Sifan, Roberts, Gareth O., Yang, Jun
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.11066
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author Grazzi, Sebastiano
Liu, Sifan
Roberts, Gareth O.
Yang, Jun
author_facet Grazzi, Sebastiano
Liu, Sifan
Roberts, Gareth O.
Yang, Jun
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_11066
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Sub-Cauchy Sampling: Escaping the Dark Side of the Moon
Grazzi, Sebastiano
Liu, Sifan
Roberts, Gareth O.
Yang, Jun
Computation
Methodology
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.
title Sub-Cauchy Sampling: Escaping the Dark Side of the Moon
topic Computation
Methodology
url https://arxiv.org/abs/2601.11066