Stereographic Markov Chain Monte Carlo

Publikation: Working paperPreprintForskning


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  • Yang, Jun
  • Krzysztof Łatuszyński
  • Gareth O. Roberts
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 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 mixing time decreases with dimension.
UdgiverarXiv preprint
Antal sider86
StatusUdgivet - 24 maj 2022
Eksternt udgivetJa


  • stat.CO, stat.ME, stat.ML

ID: 361432294