How do I know when to use which Monte Carlo method?

Question

I'm a bit confused with extensive number of different Monte Carlo methods such as:

• Hamiltonian/Hybrid Monte Carlo (HMC),
• Dynamic Monte Carlo (DMC),
• Markov chain Monte Carlo (MCMC),
• Kinetic Monte Carlo (KMC),
• Dynamic Monte Carlo (DMC)
• Quasi-Monte Carlo (QMC),
• Direct Simulation Monte Carlo (DSMC),
• and so on.

I won't ask for the exact differences, but why are all of them called Monte Carlo? What do they all have in common? Can they all be used for AI? E.g. which one can be used for gaming (like Go) or image recognition (resampling)?

Answer 1

They are all called Monte Carlo because all of them are a different version of the canonical Monte Carlo algorithm.

The canonical version of Monte Carlo algorithm is a stochastic algorithm to determine an action based in a tree representation. The differences among all these version are their exploration and exploitation mechanisms, and it is necessary to analyse each of them to define which one fits in your case.