Split Rhat question

Modeling
1

Dear all,

I hope this email is finding all of you well. I have a few (hopefully) simple questions regarding the split Rhat.

  1. The Stan output states that “…and Rhat is the potential scale reduction factor on split chains (at
    convergence, Rhat=1).” Can I presume that this is the maximum of the rank-normalized split Rhat and rank normalized folded split Rhat?

  2. The notation shows a term var^+. Is there any significance to the + sign?

  3. Is the rhat shown in the output (using the print command) the same as the rhat() function.

  4. In the example on pg. 284 of Andrew’s book, if I had n=500 iterations, the split Rhat is calculated on n=250. What happened to the other 250?

Thanks in advance,

David

2

With split Rhat, you split each chain into two and then just pretend you have twice as many chains as you did originally and see if they mix. So if you started with 4 chains of 500, you break them in two and have 8 chains of 250.

My guess is that is just emphasizing that variance estimate is supposed to be an overestimate. Not sure though.

This is what happens in the reference code, but I am not sure about the status of all the interfaces: https://github.com/avehtari/rhat_ess/blob/master/code/monitornew.R#L306

I’ll have to leave the other questions @avehtari

3

Which interface and which version? rhat() function from where?

Yes