Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo

Understand

This paper presents a detailed theoretical analysis of the Langevin Monte Carlo sampling algorithm recently introduced in Durmus et al.

• (Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau, 2016) when applied to log-concave probability distributions that are restricted to a convex body $\mathsf{K}$.
• This method relies on a regularisation procedure involving the Moreau-Yosida envelope of the indicator function associated with $\mathsf{K}$.
• Explicit convergence bounds in total variation norm and in Wasserstein distance of order $1$ are established.