MCMC Metrics

[Marcel-Rodekamp]

I would like to collect a few metrics which we should implement for the HMC (or other MCMC implementations we'll have).

• Acceptance Rate
• Auto correlation (e.g. equation 16)
• Re S distribution, evolution
• Im S distribution, evolution
• Statistical power

I am also thinking about having some of them standard and others being optional.

[evanberkowitz]

I guess one question is: when do you want to collect it? The distributions, statistical power, acceptance rate, autocorrelation of course can only be collected at the end.

I think we should frame this as: what do we need to keep track of for a given proposal / update step in order to get what we want. To make an analogy with your list:

• dH (can be translated into acceptance probability)
• [no analogy, but if you take the linked reference's claim that all correlation times converge to p_rej, I guess whether the proposal was accepted or rejected]
• Re S
• Im S
• [no analogy, but what you want is constructed from the distribution of Im S]