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?

Why isn't it in BUGS? Because nobody's peogrammed it! Or that Andrew Thomas didn't like it for some reason.

Now BUGS is open source, anyone can try to implement it. I guess you could adapt the metnormal code.

Bob

Hybrid MCMC (or the Hamiltonian MCMC algorithm) is in OpenBUGS developer. It works for quite large blocks of random effects (say 250 nodes). The method needs the first derivatives of the conditional distribution. These can not always be calculated by BUGS. I have a modified for of the algorithm that uses numerical derivatives (it is slowish…). Does anyone have theory for this modification?

I would also be itinterested in hybrid MCMC for spatial random effects (the CAR prior) and sparse data. How does it compare with the langevin MCMC algorithms?

Moi Andrew

Hybrid MCMC is used in AD Model Builder which is now freely available at

http://admb-project.org/

I used it for this problem

https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=in…

This is beta regression with random effects for which bugs does not seem to work well (according to the poster)

It seemed to give good results.

I would be happy to compare them with bugs if anyone is interested.