generalizing R-hat to ragged arrays

[Bob Carpenter]

R-hat involves a couple of averages over chains.
My question is whether I should make those weighted
by the size of the chain or not.

I've attached a PDF.

- Bob

[Andrew Gelman]

Hi, Bob. In a multilevel modeling context the weights would be a compromise (of course) between weighting the chains equally and weighting proportional to sample size. But here we want a reasonable hack, I think. My intuition is that equal weighting is safest.
A

> <ragged-rhat.pdf>

[Bob Carpenter]

On 5/22/12 8:56 PM, Andrew Gelman wrote:
> Hi, Bob. In a multilevel modeling context the weights would be a compromise (of course) between weighting
> the chains equally and weighting proportional to sample size.

> But here we want a reasonable hack, I think.

That, or it's Stan models all the way down.

> My intuition is that equal weighting is safest.

That's what it felt like to me, too.
I was worried that weighting by size would
let one long chain dominate a bunch of shorter
ones, which isn't what we want in a diagnostic.

OK -- your turn to think of something to talk
about at the Stan meeting :-)

We can talk about the IES grant afterward. I'd like
to find some good motivating categorical models.
Especially ones where it's not easy or practical to sum
out the categorical parameters.

- Bob

[Andrew Gelman]

B
I'm not sure about categorical but I talked with some astronomers today about some models that we could fit with them in Stan. They said they could program the log-posterior in C++ but it might make sense for them to talk with you directly, or we could start by sending them the Stan manual (is it online?) and they could see how far they could go writing the model in the stan modeling language.
A

[Bob Carpenter]

I'm happy to talk to them and/or send the manual.

The LaTeX for the manual's online and when we do
the release, we'll release v 1.0 of the manual, too.

In writing the log posterior, they need to be
able to do it with just the functions we provide
or functions they write in terms of ones we provide,
which are documented in the manual. That means
no Bessel functions or other such shenanigans!

- Bob

[Michael Betancourt]

But we could always code the gradients directly, in which case we could use the recursion relations for the Bessels. In any case these models are likely spatial convolutions of messy detector arrays with Gaussian (Poisson if they're being careful) noise so such matters shouldn't be much of an issue. I'd be more than happy to help in the quelling any astronomer shenanigans.

I'd be happy to decode any

[Bob Carpenter]

I didn't mean to dis' the astronomers!

It's just that we've only gone so far in
coding exotic derivatives (though Daniel's
been pushing the envelope lately).

We can certainly add stuff in as it's necessary
and we can figure out how to code the gradients.

- Bob