Threshold for R-hat (1.01 or 1.05)

Summary:

In rstan:::throw_sampler_warnings() and on the help page for rstan::Rhat(), the threshold of 1.05 is used/recommended for checking the "new" R-hat, whereas 1.01 is the threshold recommended at other (more recent?) places. I am uncertain whether rstan's current behavior is intended or a bug.

Description:

It seems like 1.01 is the currently recommended threshold for the "new" R-hat (as proposed by Vehtari et al. (2020) and as implemented in rstan::Rhat()), see Vehtari et al. (2020) and the Brief Guide to Stan's Warnings. However, in rstan:::throw_sampler_warnings() and on the help page for rstan::Rhat(), the (older) threshold of 1.05 is used or recommended, respectively. Is this intended or a bug?

Btw, the reference for Vehtari et al. (2020) needs to be updated at some places:

• the help page for rstan::Rhat()
• the "Brief Guide to Stan's Warnings"
• ... (perhaps other places)

Reproducible Steps:

May be seen from the source code of rstan:::throw_sampler_warnings() and ?rstan::Rhat.

Current Output:

Not applicable.

Expected Output:

Not applicable.

RStan Version:

I have 2.19.3 installed, but this also seems to apply to 2.21.1.

R Version:

This is independent of the R version.

Operating System:

This is independent of the OS.

Compare the threshold in rstan:::throw_sampler_warnings() with the implementation and help page for rstan::Rhat(), then review the linked Brief Guide to Stan's Warnings and Vehtari et al. (2020). Determine the intended recommendation and update the inconsistent warning behavior, documentation, and references so they agree.