SUMMARY OF DISCUSSION DURING CHOP-NOD ANALYSIS TELECON OF SEPT. 5

Mike, Martin, Lero, Giles

I reviewed the rationalle for studying the internal consistency of the
data for a given source, and specifically for computing the
reduced-chi-squared, which is a measure of this.  Along these lines, I
noted that the IRAS-20126 data show promise, but that the consistency from
night to night seems not as good as expected from the sharpinteg-computed
errors, so we need to somehow account for this before publishing.  The
reduced chi-squared computation provides a way to inflate the errors to
match the results of the internal-consistency evaluation.

I argued that such a procedure, which amounts to quantifying an unknown
source of error above and beyond the sharp-integ errors, is reasonable.  
This is because one does not necessarily expect the sharp-integ errors,
determined from the individual chopper cycles, to propagate all the way to
the final results.  I reviewed several reasons for why additional errors
might be expected.

Martin asked if SHARC-II shows such additional errors, and if SHARC-II
analysis incorporates them into the final error-bars.  The answer may be
that, because of the way that iterative methods work, the discrepancies
between flux measurements and the final source map are incorporated in a
natural way into the final error-bars.  SHARP does not (yet) have a way to
incorporate discrepancies between individual polarization measurements and
the final polarization map into the final errors.

Lero asked if there was a way to delete discrepant data and I said that we
currently have no way to do this, except for short glitches detected
during processing of the 30 ms samples within the individual chopper
cycles.

We talked about M82 analysis:

We reviewed Lero's E-mail of July, when he found 2-sigma vectors at the
peak of M82 running perpendicular to and at 45 degrees to the plane of
M82, quite different from the posted 2-sigma results for the January 2006
run, where they were parallel (for most of the posted maps).  This may be
another example of measurements not agreeing as well as they would be
expected to, given the errors.

There seems to be significant data on M 82 from both April runs.  Hiroko
analyzed some of it.  However, for the April runs we have no pointing
model.  So we can't do pointing corrections on the April M82 data.  This,
and the need for a reduced-chi-square estimate, are the biggest stumbling
blocks for M82 analysis.

Lero will look into two different ways to get the pointing corrections for
early- and late-April observations of M82:

- use Larry's elliptical fits to M82 - the ones Larry got working using
John's IDL routines in Summer 2006.

- Coordinate with Darren to develop pointing models for these runs.

We talked about the reduced-chi-squared computation and I outlined one way
to do it:

Note: This assumes that John can put a flag into sharpcombine that will
make it output Q and U and sigma-Q and sigma-U instead of q and u and
sigma-q and sigma-u.

Then:

1. Break the data set into 5 bins (for example) and compute
[Q,U,sigma-Q,sigma-U] for each data set.

2. Write a package that will do the fits algebra to compute the
reduced-chi-squared map for the data set from the above 20 maps.  (The
final reduced-chi-squared for the source is then set equal to the
map-average.)

One complication is that each of the 5 maps will have different sky
coverage so one has to reduce each fits image to correspond a sky region
that is covered by all maps.

One additional benefit is that the same package - with only very minor
changes - can be used to examine any given file to see what *its* reduced
chi squared is, with respect to the final [Q,U,sigma-Q,sigma-U] for the
source.  This way we can reject discrepant cycles, if necessary.