I was reading Christian Robert’s Blog today and quite liked the new Metropolis-Hastings algorithm he was discussing. It seemed simple and easy to implement.

Whenever I code up MCMC, I tend to stick with very basic MH algorithms, such as independent moves or random walks on the log scale.

What MH algorithms do people routinely use? In particular:

- Why do you use them?
- In some sense you must think that they are optimal – after all you use them routinely! So how do you judge optimality: ease-of-coding, convergence, …
I’m particularly interested in what is used in practice, i.e. when you code up your own schemes.

**Answer**

Hybrid Monte Carlo is the standard algorithm used for neural networks. Gibbs sampling for Gaussian process classification (when not using a deterministic approximation instead).

**Attribution***Source : Link , Question Author : csgillespie , Answer Author : Dikran Marsupial*