Stereographic Markov Chain Monte Carlo
| Autor: | Yang, Jun, Łatuszyński, Krzysztof, Roberts, Gareth O. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | High-dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves results in empirically observed ``stickiness'' and poor theoretical mixing properties -- lack of geometric ergodicity. In this paper, we introduce a new class of MCMC samplers that map the original high-dimensional problem in Euclidean space onto a sphere and remedy these notorious mixing problems. In particular, we develop random-walk Metropolis type algorithms as well as versions of the Bouncy Particle Sampler that are uniformly ergodic for a large class of light and heavy-tailed distributions and also empirically exhibit rapid convergence in high dimensions. In the best scenario, the proposed samplers can enjoy the ``blessings of dimensionality'' that the convergence is faster in higher dimensions. Comment: 80 pages, 20 figures |
| Databáze: | arXiv |
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