We introduce a new family of robust gradient-based MCMC samplers under the framework of stereographic MCMC (Yang et al. 2022) which maps the original high dimensional problem in Euclidean space onto a sphere. Compared with the existing Stereographic Projection Sampler (SPS) which is of a random-walk Metropolis type algorithm, our new family of samplers is gradient-based using the Barker proposal (Livingstone and Zanella, 2022), which improves SPS in high dimensions and is robust to tuning. Meanwhile, the proposed algorithms enjoy all the good properties of SPS, such as uniform ergodicity for a large class of heavy and light-tailed distributions and "blessings of dimensionality".

Joint work with Krzysztof Łatuszyński, Gareth O. Roberts, and Jeffrey S. Rosenthal.