Reversible Markov Chain

Reversible Markov chains are fundamental stochastic processes used extensively in various fields, primarily for sampling from complex probability distributions. Current research focuses on developing efficient algorithms, such as reversible-jump Markov chain Monte Carlo and piecewise deterministic Markov processes, to improve sampling speed and accuracy, particularly for high-dimensional problems and those involving constraints. These advancements are impacting diverse areas, including Bayesian inference for complex models like neural networks and hypergraph neural networks, and enhancing the efficiency of reinforcement learning algorithms through techniques like time-symmetric data augmentation. The development of more robust and scalable methods for sampling from complex distributions using reversible Markov chains continues to be a significant area of active research.