Hamiltonian Monte Carlo: How Momentum Turns Random Walks into Efficient Sampling Most Bayesian models are easy to write down and hard to sample from. You can usually evaluate an unnormalised posterior density, or its gradient, but you cannot draw independent samples from it directly. Markov chain Monte Carlo (MCMC) solves this by constructing a chain whose long-run distribution is the target. The question is how efficiently that chain explores. Hamiltonian Monte Carlo (HMC) is one of the ...