MCAT Position Errors (March 2006)
05apr'06: I reran a set of 416 MIS visits allowing match pairs with separations up to 7 arcseconds and any probability. I restricted the set to only include visits with at least 1000 seconds. From these data, it is reasonable to set the probability limit at 10^-5 and separation limit at 5 arcseconds: 
  galexmerge ... -prob 0.00001  -sep 5.0
Assuming TOT_IBF_ERR=0.53, here is a distribution of probabilities: prob2_1.ps . And at the low end: prob2_2.ps . We can see how log of the probability depends on separation for bright, compact sources: sep_prob_1.ps . There is a much wider distribution if we include faint sources: sep_prob_2.ps . And if we allow sources with wide FWHM we get: sep_prob_3.ps . Even in this case, the number of source pairs allowed (prob > 10^-5) between 4 and 5 arcseconds is relatively small ( 1.5% ), and the number of source pairs not allowed with prob>10^-5 and sep>5. is 0.15%.
After fixing the probability computation bug (nu=1 instead of nu=2) and correctly computing the x,y positional errors (straight average, not quadrature), I compute new values of: 
      TOT_IBF_ERR  N_FLDERR  F_FLDERR
New      0.53       0.43      0.69
Old      0.51       0.42      0.68

Here is a plot of sigmas compared with a gaussian distribution for matched pairs (NUV,FUV): New_ibf_sigmas.ps . Here is a plot of Chi-Squared probabilities for matched pairs (NUV,FUV): New_ibf_prob.ps . The excess of small probability values indicates either false matches or non-gaussian wings to the error distribution: New_ibf_prob_zoom.ps . Here is how probability varies with separation: New_Sep_Prob.ps .

A reasonable probability cutoff might be 0.001 .

Chi-squared for interband match probability: derivation.txt .
Summary of delta detectory x and y relative to sloan and between bands: ddxy_summary.txt .

This analysis was done on the latest MIS imaging data ( 90 visits in /home/runes11/tim/work/cal3bigrun/01-vsn/*/d/00-visits/*-img/02-try/ ) with the most current NLC and flat field.

We need to compute three parameters for the bandmerger: The interband field error (IBF_ERR = TOT_IBF_ERR/sqrt(2)), the NUV field error (N_FLDERR), and the FUV field error (F_FLDERR). The total radial interband position error is given by: 

(Total Radial Position Error)^2 = TOT_IBF_ERR^2
                                + (NUV radial Poisson Error from SExtractor)^2
                                + (FUV radial Poisson Error from SExtractor)^2

The above error is used to compute the probability of a NUV position and FUV position representing the same source. The NUV and FUV radial position errors are given by: 

(NUV Radial Position Error)^2 = N_FLDERR^2 + (NUV radial Poisson Error from SExtractor)^2
(FUV Radial Position Error)^2 = F_FLDERR^2 + (FUV radial Poisson Error from SExtractor)^2

These last two are the position errors relative to an absolute (true) reference frame. SDSS source positions are used to provide the true frame.

To compute the TOT_IBF_ERR, values are tried and a comparison is done between the actual separations divided by the computed total radial position error (sigmas) and a gaussian distribution. Here is a comparison of a few different values: new-compare.ps . The best solution is TOT_IBF_ERR=0.51, see: new-tot_ibf_err.ps . (This implies IBF_ERR=0.36 arcseconds.) For this analysis, an abridged list was used: n/fuv_mag >16, <21, n/fuv_fwhm_image <10 arcseconds, and fov_radius < 0.55 degrees.

The previous NLC and flat field gives a best TOT_IBF_ERR of 0.72 arcseconds ( pre-tot_ibf_err.ps ).

SDSS positions were used to derive NUV-to-truth and FUV-to-truth separations. The results for all three parameters before and after the new NLC and flat field are: 

         TOT_IBF_ERR  N_FLDERR  F_FLDERR
Pre-NLC     0.72       0.61      0.63
New-NLC     0.51       0.42      0.68
Which shows a significant improvement in NUV-FUV and NUV-truth, but FUV-truth actually gets a little worse. 
New parameters for galexmerge:  -N_FLDERR 0.42  -F_FLDERR 0.68  -IBF_ERR 0.36
Plots for Pre-NLC:

pre-nuv-sdss-sep-abr.ps  : [0.74] NUV-SDSS Separations (Abridged Source List)
pre-fuv-sdss-sep-abr.ps  : [0.86] FUV-SDSS Separations (Abridged Source List)

 pre-nuv-fuv-sep-abr.ps  : [0.94] NUV-FUV Separations (Abridged Source List)
 pre-nuv-fuv-sep-mat.ps  : [1.57] NUV-FUV Separations (All Matched Sources)

 pre-tot_ibf_err.ps      : [0.72] NUV-FUV Sigmas (Abridged List)
 pre-n_flderr.ps         : [0.61] NUV-SDSS Sigmas (Abridged List)
 pre-f_flderr.ps         : [0.63] FUV-SDSS Sigmas (Abridged List)
Plots for New-NLC:

new-nuv-sdss-sep-abr.ps  : [0.53] NUV-SDSS Separations (Abridged Source List)
new-fuv-sdss-sep-abr.ps  : [0.90] FUV-SDSS Separations (Abridged Source List)

 new-nuv-fuv-sep-abr.ps  : [0.69] NUV-FUV Separations (Abridged Source List)
 new-nuv-fuv-sep-mat.ps  : [1.24] NUV-FUV Separations (All Matched Sources)

 new-tot_ibf_err.ps      : [0.51] NUV-FUV Sigmas (Abridged List)
 new-n_flderr.ps         : [0.42] NUV-SDSS Sigmas (Abridged List)
 new-f_flderr.ps         : [0.68] FUV-SDSS Sigmas (Abridged List)
Plots of Poisson Errors:

   new-nuv-pperr-abr.ps  : [0.17] NUV Poisson position errors (Abridged Source list)
   new-nuv-pperr-mat.ps  : [0.59] NUV Poisson position errors (All Matched Sources)
   new-nuv-pperr-all.ps  : [0.89] NUV Poisson position errors (All Sources)

   new-fuv-pperr-abr.ps  : [0.15] FUV Poisson position errors (Abridged Source list)
   new-fuv-pperr-mat.ps  : [0.56] FUV Poisson position errors (All Matched Sources)
   new-fuv-pperr-all.ps  : [0.64] FUV Poisson position errors (All Sources)

           new-fwhms.ps  : FWHM values (Abridged Source List).
Here is a plot of the SExtractor Poisson position error vs. the magnitude error (inversely proportional to S/N): magerr_v_pperr .