Chapter 14 of Rethinking 2

[AlexAndorra]

Ready for review 🍾
There is a lot of new material in this chapter. Most of these novelties are in sections 3 (instrumental variables), 4 (social relations models) and 5 (GPs), so I'd recommend focusing most of the reviewing efforts there.
Thanks in advance for the reviews 🖖

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[canyon289]

Did a quick skim and things generally look good. Will do a deeper review this week, hopefully in next couple of days

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aloctavodia commented on 2020-06-29T16:01:19Z
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Typo "extracts the stds and matrix"

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aloctavodia commented on 2020-06-29T16:01:20Z
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Reading this I remember I have an unanswered question (https://github.com/aloctavodia/BAP/issues/68) :man-facepalming:

Shouldn't this be

np.exp(- 0.5 * post["rhosq"][::50].values[:, None] * x_seq ** 2)

and in the model definition

cov = etasq * pm.gp.cov.ExpQuad(input_dim=1, ls_inv=rhosq)

In the book rhosq=1.31, 1.31*0.5=0.65 (the value in this notebook), so maybe the only missing part is multiplying by 0.5

AlexAndorra commented on 2020-06-29T18:32:50Z
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Indeed, this makes sense, thanks for catching this! Also, good to know we can parametrize the ExpQuad kernel with ls_inv!

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aloctavodia commented on 2020-06-29T16:01:21Z
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typo "..And we can easily use this function in our model below" or "..And we can easily call this function in our model below"

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aloctavodia commented on 2020-06-29T16:01:22Z
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Typo "...which is why I changed it" or "that's why I changed it"

[AlexAndorra]

Indeed, this makes sense, thanks for catching this! Also, good to know we can parametrize the ExpQuad kernel with ls_inv!

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[AlexAndorra]

Thanks for the review @aloctavodia ! I corrected the typos and implemented the changes on the GP for Oceanic tools model. It turns out that:

• the prior for rhosq is super important as there isn't a lot of data. I changed it from Exponential(0.5) (as in the book) to HalfNormal(2) and results are looking much closer to the book, as does the posterior for rhosq.
• I was using Dmatsq (squared distance) instead of Dmat (simple distance) to evaluate the GP.
• In posterior predictive plots, it looks like etasq and rhosq should not be squared: they are implicitly modeled as the square in the model -- notice that Richard doesn't square them in his implementation of cov_GPL2.
• Multiplying by 0.5 to make PPC plots look closer to the formula for ExpQuad kernel does improve the results -- note however that Richard doesn't do that in his implementation 🤷‍♂️

I think that there are subtle differences in the GP implementations between PyMC and ULAM that make a bijective match hard to get, but I think this looks quite good now!
If you agree with my changes, I'll rerun the whole NB and reformat it properly 🖖

[AlexAndorra]

@aloctavodia, as discussed I just pushed the change where rhosq = pm.Deterministic("rhosq", 0.5 * ls_inv ** 2). This has the nice of property of recovering the exact formula for the ExpQuad kernel, but makes the results less similar to the book's.
This looks good enough to merge though, and we can refine the implementation even more later. Also, I reran the whole NB.
Thanks for the review 🖖

[aloctavodia]

There is a change to chapter 11's notebook that should not be part of this PR, right?

[AlexAndorra]

Yeah it should -- it's just a super tiny typo fix, so I figured it wasn't worth a dedicated PR. Thanks for approving --> merging! 🍾