Metropolis Hastings

The Metropolis-Hastings algorithm is a Markov Chain Monte Carlo (MCMC) method used to sample from complex probability distributions, particularly those where direct sampling is intractable. Current research focuses on improving its efficiency and applicability in diverse fields, including developing variants like the Metropolis-adjusted Langevin algorithm and stochastic Metropolis-Hastings for faster convergence and handling high-dimensional spaces, as well as exploring its use in conjunction with neural networks and deep generative models. This algorithm's significance lies in its broad applicability across scientific disciplines, enabling accurate statistical inference and improved model training in areas ranging from machine translation and anomaly detection to Bayesian inference and spiking neural network training.