Add chapter on multiple imputation.

[abner-hb]

Submission Checklist

• Builds locally YES
• New functions marked with <<{ since VERSION }>> YES (no new functions)
• Declare copyright holder and open-source license: see below

Summary

Add a chapter on multiple imputation to the Stan User's Guide.

Copyright and Licensing

Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company): Abner Heredia Bustos

By submitting this pull request, the copyright holder is agreeing to license the submitted work under the following licenses:

• Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
• Documentation: CC BY-ND 4.0 (https://creativecommons.org/licenses/by-nd/4.0/)

[WardBrian]

Hi @abner-hb, thanks for this! I just made a couple commits to remove the changes to the built docs -- we let our Jenkins jobs build those for us during releases.

I'll ask @bob-carpenter to take a look at the contents when he gets a chance

[bob-carpenter]

I can review this.

[bob-carpenter]

Thanks so much for contributing this.

I am really sorry that I left 73 comments on such a short chapter. It was meant pedagogically and I hope it helps other things you write. It took a couple years of this kind of back-and-forth with Gelman and Vehtari and Goodrich before they stopped marking up everything I wrote this way. Gelman and Vehtari are excellent role models for writing clarity.

If you'd rather not do this, I'm happy to make all the changes I suggested myself.

[bob-carpenter]

I just skimmed Chapter 18. Gelman et al. do not provide a fully Bayesian perspective, he instead uses multiple imputation. The fully Bayesian perspective is given in the User's Guide chapter on missing data.

I would also put this into the main text. Only use footnotes in doc as a last resort.

[abner-hb]

It's not fully Bayesian but isn't it partially Bayesian?

[bob-carpenter]

I think it's fair call it "approximately Bayesian," as that's how Gelman talks about anything from maximum likelihood point estimates to VI.

[bob-carpenter]

bayesian -> Bayesian

The model doesn't have any feedback or flow per se---it's just how joint distributions work.

[bob-carpenter]

Remove comments.

[bob-carpenter]

OK, rather than filling this all in, I'd just write a one-line summary and point to Plummer's article.

[abner-hb]

Do you mean summarizing Plummer's quote in one line? Or to summarize this entire section on cut models to one or two lines?

[bob-carpenter]

I went over this again and marked many of the grammatical nitpicky comments as resolved. I think they'd be better the way I was suggesting, but it's more important to actually publish this.

If you don't want to make these changes, @abner-hb, just let me know and I can go and make them myself.

I really appreciate your taking the time to write this despite the huge flurry of comments I've left. I hope they've been more helpful than frustrating, as that was my intention.

[bob-carpenter]

this needs {B}ayesian in the title or "Bayesian" will get lower-cased.

We generally don't need the url, doi, or publisher, but they're OK to leave in.

And thanks for citing Martyn's paper.

[bob-carpenter]

You might want to note to continue line 52 that this depends on a model of $x$, which you typically don't have with a regression, because the inferences for parameters are independent of the model of $x$ when $x$ is fully observed.

[abner-hb]

See the new paragraph at line 60 below.