Implement histogram representation

[aimalz]

For the sake of comparing the quantile representation to more conventional representations, I should implement a PDF.histogram function. Similarly, I want be able to initialize a PDF object with any one of truth, quantiles, or histogram and then convert truth into both alternatives, quantize a histogram, and histogram quantiles. I'm not sure if this should be part of the Epic and/or ready before launch of the first version or if it can wait.

[drphilmarshall]

I think it's important enough to include in v1.0. Note that if you implement a `sample()` method that fills up a pandas data frame of `PDF.samples`, you'll then be able to make histograms of those samples in place. And of course you should be able to initialize a PDF object with samples too... I think you're going to want some indicator kwargs, so that you can write ``` PDF.sample(from='truth') PDF.approximate(using='quantiles') PDF.sample(from='quantiles') ``` and so on. It's OK to have the methods refuse in cases where the implementation is incomplete. Sampling from truth is more urgent than sampling from histograms, for example - so you could punt the latter for now.

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On Fri, Dec 2, 2016 at 9:25 AM, Alex Malz ***@***.***> wrote: For the sake of comparing the quantile representation to more conventional representations, I should implement a PDF.histogram function. Similarly, I want be able to initialize a PDF object with any one of truth, quantiles, or histogram and then convert truth into both alternatives, quantize a histogram, and histogram quantiles. I'm not sure if this should be part of the Epic and/or ready before launch of the first version or if it can wait. — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#23>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AArY97FQ089_VR_4XbJ7BIug50klywaPks5rEFSbgaJpZM4LCyuR> .

[aimalz]

Good idea! I made #24 a separate issue for samples. I've already written code that samples from a histogram representation, so that won't be hard to implement.

[drphilmarshall]

Bravo! It's so nice to close issues :-)

[drphilmarshall]

OK! Histogram code is merged, and results can be seen here. Looks like evenly spaced histogram bins beats evenly spaced quantiles in the simplest possible test case: time to move to better spaced quantiles and more interesting test cases, I think!

[aimalz]

I think quantiles are really going to shine when there's small-scale structure. I want to extend the code to take more non-trivial truth functions, but that's a pretty major change requiring additional infrastructure, so I don't think I can do it by the version 1.0 launch date.

[drphilmarshall]

Ok fair enough! That means the DESC note issue should be reassigned to a later milestone then - maybe one of its own? In the meantime, should we try for any kind of better quartile distribution? I feel like uniform spacing is a bit disappointing in the wings... Re: non-trivial truth functions: shall we start with mixtures of Gaussians?

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On Wednesday, December 7, 2016, Alex Malz ***@***.***> wrote: I think quantiles are really going to shine when there's small-scale structure. I want to extend the code to take more non-trivial truth functions, but that's a pretty major change requiring additional infrastructure, so I don't think I can do it by the version 1.0 launch date. — You are receiving this because you modified the open/close state. Reply to this email directly, view it on GitHub <#23 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AArY99yuqP-C9WRoJEu4RBbGYiS3wft6ks5rFzemgaJpZM4LCyuR> .

[aimalz]

Excellent point! I've addressed non-uniform quantile spacing in #38.

Re: non-trivial truth functions, starting with mixtures of supported scipy.stats.rv_continuous objects seems extremely reasonable.