From: Robert A. Knop Jr. (robert.a.knop@vanderbilt.edu)
Date: Tue Feb 25 2003 - 14:36:24 PST
(Tony -- could you please alert the relevant people that this has shown
up on the archive page?)
The argument was made during the group meeting, and at the time I
believed it, that I should be marginalizing rather than intersecting to
get the best value of Omega_M for a flat universe.
I no longer think this is correct.
Omega_M for a flat universe means, if you assume Omega_M+Omega_Lambda=1,
what is the best fit value you get for Omega_M? The way to address this
is to do a chi-square fit of the cosmology, allowing Omega_M to vary.
Specifically, I would calcualte chisquare for lots of values of Omega_M,
and at each value use 1-Omega_M for Omega_L in the luminosity distance
calculation. What this would produce is *exactly* the *intersection* of
our confidence regions with the Omega_M + Omega_L = 1 line.
Marginalizing is something weird. To get the value in question, one
would Marginalize over the parameter Omega_M+Omega_L to find the best
value of Omega_L-Omega_M; call that result x. The "best fit Omega_M
assuming flat" would them be (1-x)/2. However, that's not really what
that is; that's just another way of saying what is the best fit value of
Omega_L-Omega_M, where Omega_L+Omega_M can have any value. That's
something perverse that isn't really directly what we care about in this
case.What we're *really* interested in is what is the best fit value of
Omega_M, given that Omega_M+Omega_L is constrained to be equal to 1.
Thus, we want to intersect, and not marginalize, in order to determine
the "assumed flat universe" value of Omega_M.
-Rob
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