Single Epoch Likelihood

I've been playing with the single epoch likelihoods cross checked with the truth table. The rest of the targeting will be on single epoch measurements (i.e. not stripe 82) so these are a more accurate measurement of how well the likelihood is doing. I've been playing with adjusting various parameters like how we define "variability" in terms of the chi^2 cut, if we should add variable objects from the L_everything catalog to L_QSO.

Below are the raw numbers of quasars targeted (normalized to targeting of ~40/degree^2) as well as the accuracy of each method:

No variability Method
; number quasars
1029
;percent accuracy
0.545986
; total targeted
1881


Variable objects with chi^2 > 1.5 subtracted from L_everything
; number quasars
1047
;percent accuracy
0.556619
; total targeted
1881


Variable objects with chi^2 > 1.5 subtracted from L_everything
Variable objects with chi^2 > 1.5 added to L_QSO
; number quasars
1033
;percent accuracy
0.549176
;total targeted
1881


Variable objects with chi^2 > 1.1 subtracted from L_everything
; number quasars
1053
;percent accuracy
0.559809
; total targeted
1881



Variable objects with chi^2 > 1.2 subtracted from L_everything
; number quasars
1055
;percent accuracy
0.560872
; total targeted
1881


Variable objects with chi^2 > 1.3 subtracted from L_everything
; number quasars
1054
;percent accuracy
0.560340
; total targeted
1881


Variable objects with chi^2 > 1.4 subtracted from L_everything
; number quasars
1051
;percent accuracy
0.558745
; total targeted
1881


Variable objects with chi^2 > 1.2 subtracted from L_everything
Variable objects with chi^2 > 1.6 added to L_QSO
; number quasars
1036
;percent accuracy
0.550771
;total targeted
1881

Variable objects with chi^2 > 1.2 subtracted from L_everything
Variable objects with chi^2 > 1.5 added to L_QSO
; number quasars
1035
;percent accuracy
0.550239
;total targeted
1881

Variable objects with chi^2 > 1.2 subtracted from L_everything
Variable objects with chi^2 > 1.4 added to L_QSO
; number quasars
1034
;percent accuracy
0.549708
;total targeted
1881


Variable objects with chi^2 > 1.2 subtracted from L_everything
Variable objects with chi^2 > 1.3 added to L_QSO
; number quasars
1029
;percent accuracy
0.547049
;total targeted
1881

It seems that the method with the best accuracy (56%) is variable objects with chi^2 > 1.2 subtracted from L_everything.

Here is a plot of the L_everything (non variable) vs L_QSO:

Magenta objects are targeted QSOs.
Cyan objects are targeted stars.
Green objects are not targeted stars.
Red objects are missed qsos.

It looks like we might be able to make the L_ratio a function of L_QSO to perhaps pick up a few more of the red objects at the top right corner.

Another interested plot is looking at likelihood-ratio vs g-band flux:

The color scheme is the same as first plot

We might be able to get more missed QSOs (red) if we target faint (g-flux less than 5) objects with a L_ratio close to the cut. I've also plotted likelihood-ratio vs g-r magnitude:

The color scheme is the same as first plot

Again, we might be able to use the fact that the missed QSOs (red) are clustered.

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