Gibbs Algorithm

The Gibbs algorithm is a Markov Chain Monte Carlo (MCMC) method used for sampling from complex probability distributions, primarily targeting posterior distributions in Bayesian inference and machine learning. Current research emphasizes improving its efficiency, particularly through adaptive weighting schemes and blocked Gibbs sampling to accelerate convergence in high-dimensional spaces, such as those encountered in Bayesian neural networks and time series modeling. These advancements enhance the algorithm's applicability to diverse problems, including blind denoising, variable selection in linear models, and improved accuracy in forecasting and inverse problems. The resulting improvements in computational speed and accuracy have significant implications for various scientific fields and practical applications requiring efficient Bayesian inference.