Changeset 41181

Timestamp:

Nov 29, 2019, 11:21:52 AM (7 years ago)

Author:

eugene

Message:

stats justifications

File:

• trunk/doc/release.2015/ps1.calibration/calibration.tex (modified) (5 diffs)

trunk/doc/release.2015/ps1.calibration/calibration.tex

@@ -1038 +1038 @@
 
 As described above, the instrumental magnitude and the calibrated magnitude
-are related by arithmetic magnitude offsets which account for effects
+are related by \textmod{additive} magnitude offsets which account for effects
 such as the instrumental variations and atmospheric attenuation (Eqn~\ref{eqn:Mrel}).
 %% \begin{equation}
@@ -1089 +1089 @@
 rejections do not catch all cases of bad measurements.
 
-\note{justify this outlier rejection process}
 After the initial iterations, we also perform outlier rejections based
 on the consistency of the measurements.  For each star, we use a two
@@ -1097 +1096 @@
 \& standard deviation (weighted by the inverse error) are
 recalculated.  We then reject detections which are more than 3$\sigma$
-from the recalculated mean.  
+from the recalculated mean.
 
 Suspicious stars are also excluded from the analysis.  We exclude stars
@@ -1115 +1114 @@
 calibrated based on their overlaps with other images.
 
-\note{justify the choice of a factor of 10}
+\textadd{We note that the goal of these rejections is to avoid biasing
+  the zero points by including clearly inconsistent or poor quality
+  measurements.  The criteria have been chosen by inspection of the
+  dataset to avoid rejecting too many valid measurements, but the
+  specific numbers are admittedly ad-hoc.  However, as long as the
+  exclusions do not bias the results, the exact choices are not
+  critical.  The only exclusion we make which is not symmetric with
+  respect to the average values is the choice to reject images with
+  substantial extinction.  However, we believe this choice is
+  justified since we know real images with clouds will often have
+  significant extinction variations across the field and will thus be
+  poorly represented with a single exposure zero point.}
+
 We overweight the ubercal measurements in order to tie the relative
 photometry system to the ubercal zero points.  Ubercal images and
 measurements from those images are not allowed to float in the
 relative photometry analysis.  Detections from the Ubercal images are
-assigned weights of 10x their default (inverse-variance) weight.  The
-calculation of the formal error on the mean magnitudes propagates this
-additional weight, so that the errors on the Ubercal observations
-dominates where they are present. 
+assigned weights of 10x their default (inverse-variance) weight.
+\textadd{The choice of 10, while somewhat arbitrary, is chosen to
+  ensure that the ubercal data will dominate the result unless it
+  represents much less than 10\% of the measurements.  Since most
+  areas of the sky have at least a few epochs of ubercal data per
+  filter, only for rare regions will the non-ubercal data drive the
+  results.}  The calculation of the formal error on the mean
+magnitudes propagates this additional weight, so that the errors on
+the Ubercal observations dominates where they are present.
 
 \begin{equation}
@@ -1368 +1384 @@
 \code{http://users.stat.umn.edu/~sandy/courses/8053/handouts/robust.pdf}
 \code{https://arxiv.org/pdf/0807.0575.pdf}
+\code{https://www.redalyc.org/pdf/3939/393933924009.pdf}
+\code{Street, J. O., Carrol, R. J., \& Ruppert D. 1988, Am. Stat, 42, 152}
+\code{Green, P. J., 1984, J. R. Statist. Soc B, 42, 149}
 
 \subsubsection{Selection of Measurements}