Log-Concave Sampling

Log-concave sampling studies how to draw representative samples from distributions with convex negative log densities, a common model in Bayesian inference and constrained uncertainty estimation. Main approaches include Langevin methods, Hamiltonian Monte Carlo, proximal samplers for nonsmooth or constrained targets, and geometric walks such as Dikin walks on polytopes. Guarantees are typically measured in total variation, Wasserstein distance, or related divergences, with cost depending on dimension, condition number, smoothness, and initialization. A central challenge is achieving sharp high-accuracy guarantees from arbitrary starting points, especially when targets are constrained or nonsmooth and dimension dependence remains costly.