Hybrid Monte Carlo is not a new energy-efficient auto race. It’s a computational method developed by physicists to improve the efficiency of random-walk simulation (i.e., the Metropolis algorithm) by adding auxiliary variables that characterize the “momentum” of the simulation path. I saw Radford Neal give a talk on this over 10 years ago, and it made a lot of sense to me. (See here, for example.)
My question is: why isn’t hybrid Monte Carlo used all the time in statistics? I can understand that it can be difficult to program, but why isn’t it in software such as Bugs, where things only have to be programmed once? Even if it doesn’t solve all problems, shouldn’t it be an improvement over basic Metropolis?