First, I’ll re-introduce Metropolis-Hastings, the algorithm behind Gibbs Sampling and similar Markov chain algorithms. I assume most readers have at least heard of it. Instead of mathematical rigor, I’ll animate the approach so that the reader can appreciate both why it works and why it cannot scale with our inferential ambitions. Second, I’ll introduce Hamiltonian Monte Carlo, a very different approach to constructing Markov chains. Again, the goal is not to be mathematically precise, but to animate the algorithm and show why it works and why it still has limits.

https://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/