new density fluctuations model

[moustakas]

@geordie666 @forero I started playing around with a new target density fluctuations model using mixtures of Gaussian functions as part of #252. If you get a chance could you take a look at this notebook and send comments?

[moustakas]

Once tests pass I'd like to self-merge this, since it is needed for #261 and the only substantive change is a new notebook (linked above). Comments are still welcome but after a discussion with @geordie666 I've decided to move forward with a simple linear regression of density versus Galactic reddening. I will reach out to the Clustering WG to see if they can develop a more realistic / sophisticated model for our use.

One question for @geordie666, though: Do you know why the QSO and LRG target densities are gridded / binned in the hp-info-dr5-0.17.1.fits file (see, e.g., cells 28 and 30)?

[geordie666]

@moustakas: Can you elaborate on what you mean by gridded/binned? DENSITY_QSO and DENSITY_LRG are single numbers for a cell, so it's hard for me to see any gridding.

[moustakas]

Here is the QSO density vs EBV (directly from the "info" structure) from this notebook. Any ideas on what's giving rise to this? Shouldn't the density be a continuous variable (as it is for, e.g., ELGs and BGS)?

[geordie666]

I think this is a reasonable explanation:

At nside=256 the pixel area is 0.052456 sq. deg.

Therefore, if you have, 1, 2, 3, 4 QSOs in a pixel, etc., the density (and the log10 of the density) is as follows:

np.arange(1,10)
    array([1, 2, 3, 4, 5, 6, 7, 8, 9])

np.arange(1,10)/0.052456
    array([  19.06359616,   38.12719231,   57.19078847,   76.25438463,
             95.31798078,  114.38157694,  133.4451731 ,  152.50876925,
            171.57236541])

np.log10(np.arange(1,10)/0.052456)
    array([ 1.28020483,  1.58123483,  1.75732608,  1.88226482,  1.97917483,
            2.05835608,  2.12530287,  2.18329482,  2.23444734])

If our quasar density is ~200 per sq. deg. then in a 0.052456 sq. deg. pixel your modal number of quasars should be ~10. Certainly, there will be pixels with 1, 2, 3 etc. quasars in them.

So, I think you're just seeing discreteness from this effect. We could merge adjacent pixels if they contain fewer than X sources?

[moustakas]

Thank you, @geordie666, that explains it! I don't think it's worth merging adjacent pixels -- I think this is just an artifact of an incomplete imaging survey.