Potential Scale Reduction and chains=1

General
1

Hi, would anyone know how Stan calculates the Rhat value using only one chain?

2

I remember reading somewhere that for effective sample size calculations a single chain will be split in half. It’s probably the same for R hat.

3

Perhaps you are remembering from the Stan User Manual in the section entitled “Initialization and Convergence Monitoring”.

4

Wow! This is news to me. Thank you very much. I found something about this on page 479 of the Stan version 2.12.0 manual.

5

However, a reference about the subject would be interesting.

6

Don’t use Stan version 2.12.0 because the sampler was (slightly) broken, although the theory of split R-hat does not change in later versions. I think the only published explanation of it is in the BDA3 textbook, but Andrew might be working on a paper about it.

1 Like
7

It’s in Gelman et al.'s Bayesian Data Analysis. And Andrew’s trying to put together a paper on split R-hat and ESS calculations that discount for non-convergence.

8

Thank you, prof. Carpenter.