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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.11066 |
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| _version_ | 1866915734489137152 |
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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 |