Quantitative diagnostics for assessing the convergence of MCMC samples

General
1

Hi,

Can anyone help me with how I can have the Heidelberg-Welch diagnostic and Geweke diagnostic for the output of my model in rstan to assess the convergence of the MCMC chains?

I know there are some qualitative (graphical) diagnostics in the package of “bayesplot”, but I would like to report quantitative diagnostics like Heidelberg-Welch and Geweke diagnostics.

Any help is appreciated.

2

What interface are you using? rstan, pystan, cmdstanr, cmdstapy, or cmdstan?

All should give you HMC-specific checks for each chain (divergences, treedepth saturation, EBFMI), as well as by-parameter checks (rhat, bulk-ESS, tail-ESS).

3

Hi,

I used “rstan” interface.

4

In fact, I would like to report the Heidelberg-Welch diagnostic and Geweke diagnostic for assessing the convergence of MCMC samples corresponding to the parameters in my model.

5

Ok, we’ll those aren’t diagnostics that the core Stan developers decided to support in any of the interfaces, so you’ll have to find an R package that implements them.

I’m not super familiar with those diagnostics, but after looking them up just now they seem to be designed specifically for samplers that tend to have issues with strong auto-correlation, but HMC does not have this property. Check out the paper on the rhat that the core devs developed/recommend to see if there’s discussion as to why it’s better in the context of HMC than those you mention and maybe report back on what you find?

6

Great, thank you. I will look at the paper.