update Gaussian Mixture Model example with pm.NormalMixture

[drbenvincent]

Following discussion in #102, this is a revamp of the GMM example. The model/notebook is now considerably simpler as it uses the new pm.NormalMixture distribution.

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OriolAbril commented on 2022-04-13T15:18:48Z
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I think it could be good to add a classification tag, I assume there will be some more notebooks with mixtures or bart even that cover that.

drbenvincent commented on 2022-04-16T13:18:43Z
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done

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OriolAbril commented on 2022-04-13T15:18:49Z
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You can use xarray-einstats here:

from xarray_einstats.stats import XrContinuousRV
xi = np.linspace(-7, 7, ni)

post = idata.posterior

pdf_components = XrContinuousRV(norm, post["mu"], post["σ"]).pdf(xi) * post["w"]

pdf = pdf_components.sum("cluster")
...
x[1].plot(xi, pdf)

...
(pdf_components / pdf).plot.line(hue="cluster", ax=ax[2])

...

More details on https://einstats.python.arviz.org/en/latest/tutorials/stats_tutorial.html#probability-distributions if this looks interesting. Main highlights are that XrContinuousRV wraps the scipy distributions so they accept DataArrays as inputs, yet, the pdf/ppf/cdf... methods can still take array_like as input (it is internally converted to xarray using point or quantile as dimension name).

drbenvincent commented on 2022-04-16T13:39:35Z
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I've played about with this a bit, but the plotting is not working. I'm leaning towards keeping the existing code because it is very transparent about what is happening, and use of XrContinuousRV would only save a couple of lines of code.

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OriolAbril commented on 2022-04-13T15:18:50Z
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The verbs should stick to the https://docs.pymc.io/en/latest/contributing/jupyter_style.html#authorship-and-attribution, the dates and pr links can be skipped for old and hard to track contributions. We discussed having a more graded approach for "updated" type with "extended" or "re-written" too for example but eventually decided on only using "re-executed" and "updated" (with the definition/line on updated being very vague)

drbenvincent commented on 2022-04-16T13:25:14Z
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Have updated the verbs

[drbenvincent]

done

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[drbenvincent]

Have updated the verbs

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[drbenvincent]

I've played about with this a bit, but the plotting is not working. I'm leaning towards keeping the existing code because it is very transparent about what is happening, and use of XrContinuousRV would only save a couple of lines of code.

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[drbenvincent]

Think I've addressed all the points - although let me know about xarray-einstats. I don't think it really it's ultra compelling to use in this simple example where the plot code is pretty concise to begin with

[OriolAbril]

I forgot the means in the xarray code, so now the plot is getting a 4d array. The difference is in how the operations are done, mean first vs mean later. Ending up with some more or some less lines of code is not an issue for me, the goal is not having less lines of code, if xarray plotting is less clear let's keep the raw matplotlib plotting. I would like to use the mean later approach though, and I think einstats helps with that (it is basically a collection of things that have helped me do that throughout the last couple years)

[drbenvincent]

Ok. Tried harder with plotting through xarray and got it to work

[OriolAbril]

Looks great, thanks for taking a look at the mean later approach and getting it to work.

[drbenvincent]

Ok. Think that's done now?