Some Suggestions reagrding MCMC

Hi, Ricky Nice to read your wiki about MCMC, which helps me a lot in understanding the mutual relationship between Markov Chain and Monte Carlo. I have some questions regarding your wiki listed as follows: 1. You put a large paragraph on the proof of correctness of MH Algorithm, is there any particular reason for that? 2. Can you have more explanation on the reason for choosing different proposal distribution and their respective advantages and disadvantages? 3. You mentioned in the application that MCMC can be applied in any context where density of interest is too complex for simple sampling method can you elaborate more on your Gibbs sample because I don't see the advantage of applying MCMC on the model over other models.

Thanks Arthur

Hey Arthur,

1. The proof of correctness is essential for any MCMC algorithm, as it is the core proof behind why the law of large numbers can be applied. Generally, any variant (new) MCMC algorithm must be accompanied by such a proof. I'm just showing the basic idea behind why Metropolis-Hastings is correct.

2. Sure. Although there really isn't any, other than just using what densities are available to you.

3. That is more suited as a "problems" section for basic Monte Carlo methods, like rejection sampling. But let's see if I can add some more intuition.

Thanks for the feedback,

Ricky