H amiltonian M onte C arlo

Abstract Markov chain Monte Carlo(MCMC) is a powerful tool for approximating posterior distributions in Bayesian analysis. Traditional MCMC methods such as the Metropolis–Hastings algorithm often converge at suboptimal rates, especially in higher dimensional parameter spaces. Hamiltonian Monte Carlo (HMC) improves the efficiency of the Metropolis–Hastings algorithm using the Hamiltonian equations from classical mechanics to guide posterior sample generation. Theoretically, HMC could reach a perfect acceptance rate under ideal conditions. In practice, the actual acceptance rates tend to be influenced by various numerical factors. In this article, we describe the basic concept and practical implementation of HMC.