Proposal Distribution

Proposal distribution design is crucial for efficient Monte Carlo methods, aiming to optimize sampling from complex probability distributions by cleverly choosing a simpler distribution to guide the sampling process. Current research focuses on developing adaptive and theoretically-grounded proposal distributions, leveraging techniques like normalizing flows, annealing, and reinforcement learning to improve sampling efficiency and accuracy, particularly for rare events and high-dimensional spaces. These advancements have significant implications for various fields, including Bayesian inference, rare event simulation, and optimization problems, by enabling more accurate and efficient estimation of probabilities and model parameters. The development of optimal proposal distributions is a key challenge driving ongoing research.