Hamiltonian Monte Carlo

Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo method used for sampling from complex probability distributions, particularly those arising in Bayesian inference and machine learning. Current research focuses on improving HMC's efficiency and robustness, particularly for high-dimensional problems, through techniques like stochastic gradient HMC (SGHMC), adaptive step size and integration time adjustments, and the integration of neural networks as surrogate models to accelerate likelihood evaluations. These advancements are significantly impacting fields like astrophysics, medical imaging, and reinforcement learning by enabling more accurate and efficient Bayesian inference in challenging applications where traditional methods struggle.