Chapter 7 of Statistical Rethinking 2nd Edition

[oscarbranson]

As promised (#67) here's a first stab at Chp_07. It turned out to be a bit more of a beast than I expected, and there are a few things that aren't quite right - any corrections/pointers appreciated. You said you might be able to help, @aloctavodia?

I've stolen quite a few bits from Chapter 6 of the 1st Edition (these are cited).

There are a few comments throughout where I hit trouble, but the main ones are:

• Code 7.3-7.10 I've use MCMC here, Chapter 6 of the 1st Edition used OLS. As a result the credible intervals on Figure 7.3 are much larger here than in the book, and following LPPD estimates are quite different from numbers in the book (in absolute, not relative magnitude).
• Code 7.18 The uncertainties here are much larger than in the book (they also were in 1st Ed). I assume this is a MCMC vs. OLS problem again?
• Code 7.27-7.30 Can't work out how to reproduce the book results using the arviz.waic function. Mainly because I'm not sure how outputs of arviz.waic and rethinking's WAIC function are different. Neither documentation is particularly informative about what the functions actually calculate. A barrier in arviz.waic is that setting pointwise=True doesn't seem to return a pointwise result (returns identical if set to False) as it does in WAIC, which makes a lot of the book examples impossible. Could probably work out how to do it manually, but feels like I shouldn't have to! What have I missed?!
• Code 7.31 My solution here is ugly. Couldn't find an obvious way to calculate pairwise dSE using arviz as a single number.
• Code 7.43 Is also blocked by my confusion over the behaviour of setting pairwise=True in arviz.waic.

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[oscarbranson]

Thanks for the comments @aloctavodia. I've dealt with most of them, as well as re-done the back end of the notebook... it seems I was working from a book draft, and the final version contained quite different examples!

Just awaiting clarification on your the dataset_dict in your suggestion above, then I'll get it into merge-able state.

[oscarbranson]

OK @aloctavodia, I think I've taken care of your suggestions. Apart from the several issues that you'll probably find that need correcting, I think this is ready to merge 😄

[aloctavodia]

LGTM, I will add a semicolon at the end of the last line of matplotlib functions to avoid the ouputs. Regarding the computation of the pairwise dse. I think we can revisit it after we decide what to do in ArviZ.

[oscarbranson]

Ah! Keep forgetting about that. Just fixed it, @aloctavodia.