Page Comparison

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• Here is a plot of the residual vs redshift (no sky directional information considered). 
  • For all 4 plots:
    • The top panel shows the residuals of all individual Sn from the surveys considered 
    • The bottom panel shows the average residual in twenty bins of either even size or that contain the same number of SN (up to +/- 1) 
  • The first plot shows all surveys.  There are 20 bins of equal redshift size. 
  • The second plot shows all surveys.  There are 20 bins that contain an equal number of SN.
  • The third plot shows only the PS1 survey.  There are 20 bins of equal redshift size. 
  • The fourth plot shows only the PS1 survey.  There are 20 bins that contain an equal number of SN.
    
    
    
• Now, in order to avoid conflating signals in z with those in extinction, let's look at the above plots divided into the 10 PS1 fields 
  • In addition to PS1, the other two relatively large surveys we have data on are: SDSS and SNLS
  • There are 2 fields that have overlap between PS1 and SDSS and 3 fields that have overlap between PS1 and SNLS (no overlap between SDSS and SNLS)
• Each plot represents one field (generally ~2x2 degrees or so), so extinction is (hopefully) relatively consistent across 
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• Here are two plot for the mu residuals vs extinction (E(B-V) as measured with Finkbeiner et al: https://arxiv.org/pdf/1507.01005.pdf).  The distinct plots are similar to the residual v redshift plots above
  • For all 4 plots:
    • The top panel shows the residuals of all individual Sn from the surveys considered 
    • The bottom panel shows the average residual in twenty bins of either even size or that contain the same number of SN (up to +/- 1) 
  • The first plot shows all surveys.  There are 20 bins of equal extinction size. 
  • The second plot shows all surveys.  There are 20 bins that contain an equal number of SN.
  • The third plot shows only the PS1 survey.  There are 20 bins of equal extinction size. 
  • The fourth plot shows only the PS1 survey.  There are 20 bins that contain an equal number of SN.
    
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• Here is a plot for the mu residuals and the extinction (as measured with Finkbeiner et al: https://arxiv.org/pdf/1507.01005.pdf) on the sky. 
  • Each of the 10 PanStars1 fields are displayed twice: 
    • the top frame is the extinction (E(B-V)) 
    • the bottom is the PS1 SN, 
      • Each point represents a single SN
      • The points themselves are color-coded by normalized mu residual (ie, [mu residual] / [mu uncertainty])   
  • The right colorbar is for the extinction contour plots 
    • All extinction contour plots are on the same logarithmic scale
  • The left colorbar is for the SN scatter plots
    • All SN are on the same linear scale
  • I am not completely happy with this plot, but I am not sure what the best way to improve it is
  

Here is a first-pass at a plot showing the residual as a value of extinction and redshift together (presently for the PS1 data only). 

• The color describes the value of the residuals, divided by the errors 
• Linear interpolating is used to determine the value between points (a cubic interpolation produced some anomalously 'hot' and 'cold' regions)
• The uneven sampling in the space makes the contour plot a bit of a mess
• Another possibility might be to apply some sort of 'smoothing' to determine the value between points
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Some notes:

• • Almost all of the 1d projected plots suggest that the residuals are systematically negative.  Some quick calculations confirm this:
    • For ALL the SN mu residuals:
      • The raw mean is ~ - 0.059 (0.005)
      • The weighted mean is ~ - 0.067 (0.004) 
    • For just the PS1 mu residuals:
      • The raw mean is ~ -0.065 (0.009) 
      • The weighted mean is ~ -0.068 (0.009) 
  • Fitting seems like a good next step. Probably start with polynomials. 
  • Could also be interesting to see if patterns identified in one survey are consistent across surveys (PS1 and SDSS probably best places to look)  

CWS notes June 26 2017-

1. Perhaps make a fit of residuals vs. extinction for PanSTARRS data? By eye it looks like there is a statistically significant non-zero coherent residual at low extinction values. 
2. A different binning scheme might be equal number of SNe per bin? 
3. Another interesting plot would be contour surface of residual vs extinction and redshift, both. 

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