Hamiltonian Monte Carlo

Hamiltonian Monte Carlo (HMC) is a method for efficiently exploring complex probability distributions. It uses concepts from physics—specifically, the motion of particles—to guide how it samples possible outcomes. Imagine a ball rolling over a landscape shaped by the data; HMC simulates this motion, allowing it to move quickly through unlikely regions and focus on areas where the true distribution concentrates. This process results in more accurate and faster sampling compared to traditional methods, making it valuable for Bayesian inference and statistical modeling involving high-dimensional, intricate probability spaces.