Metropolis Adjusted Langevin Algorithm

The Metropolis-Adjusted Langevin Algorithm (MALA) is a Markov Chain Monte Carlo (MCMC) method used for sampling from complex probability distributions, particularly in high-dimensional spaces, aiming for efficient and accurate estimations. Current research focuses on improving MALA's convergence rates and efficiency, often by incorporating techniques like prior diffusion, momentum-based optimization (e.g., AdamMCMC), and handling constraints on the distribution's support. These advancements are significant because they enable more accurate and faster Bayesian inference in diverse applications, including image processing, high-energy physics, and statistical modeling, where efficient sampling from high-dimensional posteriors is crucial.