``ProxNest`` is an open source, well tested and documented Python implementation of the *proximal nested sampling* algorithm (`Cai et al. 2022 <https://arxiv.org/pdf/2106.03646.pdf>`_) which is uniquely suited for sampling from very high-dimensional posteriors that are log-concave and potentially not smooth (*e.g.* Laplace priors). This is achieved by exploiting tools from proximal calculus and Moreau-Yosida regularisation (`Moreau 1962 <https://hal.archives-ouvertes.fr/hal-01867195/file/Fonctions_convexes_duales_points_proximaux_Moreau_CRAS_1962.pdf>`_) to efficiently sample from the prior subject to the hard likelihood constraint. The resulting Markov chain iterations include a gradient step, approximating (with arbitrary precision) an overdamped Langevin SDE that can scale to very high-dimensional applications.
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