From: Alexander Conley (AJConley@lbl.gov)
Date: Mon Oct 04 2004 - 13:10:43 PDT
After some playing around it looks like my blindness scheme
doesn't work nearly as well in w space as it did in Om/Ol space.
The culprit seems to be the shape of the error contours, which are
almost pathological in the w/om plane -- at least for the SN data alone.
I do have a version that kind of works, which I will use, but
improvements will clearly have to be made if something like
SNAP tries to use this technique.
The problem comes down to how you specify the original,
non-blind values of Om/Ol (or w/Om). In the first case, after
some experimentation I discovered that the most reliable
method seemed to be to estimate Om/Ol from the 1D marginalized
probability distributions. Originally I simply used the best fitting
4 dimensional (om,ol,script_m,alpha) point, but this proved to
be a bit sensitive. The best fit could lie close to a grid point
boundary,
so sometimes a very small shift in om/ol could lead to a larger than
anticipated change. The slightly random nature of the fitting process
seemed to also contribute to some variablility. The marginalized
distributions were more stable, so I went with them.
Sadly, the marginalized distributions in w/om space (at least
for SN data only) are pretty useless. The curvature means that the
marginalized point and the best fitting 4D point are frequently rather
far away from each other (which is not true in the Om/Ol case).
The marginalized point seems to frequently end up in the tails of the
2D error contour, which isn't really surprising when one looks at it.
Another problem is that the error contour seems to run badly off to
negative om values, which I can't include in my parameter space. This
is also an issue in Om/Ol, but much less of one.
Test show that using the marginalized w/Om simply doesn't work.
Applying a shift to w/om of +0.2, -0.1 shifted the best fit values by
+0.12, -0.02, which is not sufficiently close to the desired effect by
a long shot.
Using the best fit 4D point works much better, but the previous worries
about the sensitivity to the gridding in 4D apply.
Note that I do not expect the marginalized distributions to be a problem
once the CMB, etc. priors are added. This should have the effect of
making the error contour much more normal looking, in which case
the marginalizations should be useful again.
In theory it would be possible to apply the blindness after including
these
additional priors, but I think this is a bad idea. I suspect that it
would not
be too difficult to back out some information about the secret offset if
the priors were included at this stage, particularly because the 2dFGRS
contours are so vertical in this plane. That is, I think somebody
could violate
the blindness scheme if I tried this. In order to really make this
work you
have to have end-to-end control of the results, which I don't if the CMB
and galaxy surveys are included.
In a conversation last week you suggested trying to apply some sort of
polynomial warping to 'straighten-out' the error contour. This is an
interesting idea, but since when you get right down to it I don't really
care about w for this paper, I am not going to explore it. Instead I
will
use the 4D point with the provisio that it simply isn't as stable, and
leave
the 'unbending' to somebody who really needs this information.
Alex
This archive was generated by hypermail 2.1.4 : Mon Oct 04 2004 - 13:10:42 PDT