Q-Q Plot

[aimalz]

I was thinking it might be useful to implement a quantile-quantile plot option in addition to calculating the RMS and KLD to compare PDF objects.

Edit: This will probably also merit another explanatory notebook like kld.ipynb.

[drphilmarshall]

Will this help us optimize the algorithm for choosing the quantiles? I still wonder whether regular separations could be improved upon.

[aimalz]

I'm not sure if it will help with #35, but I can imagine a way to use the q-q values to choose the optimal quantile spacing. What if we ran an optimizer over the quantiles to minimize the L1 or L2 norm between the true PDF and the quantile PDF? A corollary to this idea is that the bin endpoints could be optimized using the q-q between the true PDF and the binned PDF, which would be guaranteed to be just as good of an approximation as optimized quantiles. (The biggest remaining advantage to the quantiles would then be that the approximated PDF information could be stored more compactly. EDIT: Actually, there's no reason for me to think that -- the two options would be more or less indistinguishable under an optimization of this type. . .) I'll try it out!

[drphilmarshall]

Optimizing the quantiles is a great idea! Only connect, eh? :-) You could try optimizing the MSE/L2 norm and then compare with optimizing the KLD, and look for differences in both quality of result and computational efficiency. BTW I think you will want to do these tests on a large number of mock 1D PDFs, so you can "average over an effective ensemble of photo-z datasets". The goal is to find a _robust_ PDF approximation scheme - ie one that works in "all cases"... Weren't we going to generate mock photo-z PDFs using some mixture of Gaussian scheme? We may even have an open issue...

[aimalz]

Indeed, #36 includes mention of nontrivial PDFs, which I envisioned being mixtures of scipy.stats.rv_continuous objects. However, I haven't yet thought about deploying qp on a "survey" of mock 1D PDFs. Perhaps that should be a separate issue.

[drphilmarshall]

Yes, I think you're right - separate out the mixture of RVs capability from the simulating a survey project notebook.

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On Thu, Jan 19, 2017 at 12:31 PM, Alex Malz ***@***.***> wrote: Indeed, #36 <#36> includes mention of nontrivial PDFs, which I envisioned being mixtures of scipy.stats.rv_continuous objects. However, I haven't yet thought about deploying qp on a "survey" of mock 1D PDFs. Perhaps that should be a separate issue. — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#42 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AArY980r3z5CO9bgrMZKkmKhOM1Jtyytks5rT8g3gaJpZM4LnO6p> .