From: Don Groom (deg@panisse.lbl.gov)
Date: Thu Feb 27 2003 - 13:00:46 PST
Please forgive me for thumpiing an old tub, but the E(B-V) prior business
stirs up some deep religious matters for me...
There is a big difference between a physical quantity and the value we
measure, and they have to be kept separate. There is a "true" E*(B-V), and
our measured value E(V-B). One can say that E*(B-V)<0, but it is incorrect
to say that E(B-V) < 0. For example, suppose that E*(B-V) = 0. Then our
measured values are negative as often as positive, distributing about 0
as per our measurment uncertaintly. If we impose the requirement E(B-V)<0
on these experimental numbers, then the average is *always* postive, in
other words, badly biased. That was at least what was happening in some of
the early arguments we've had on this. If somebody introduces a prior
on E based on physics, he's pretending that E* = E. That's useful of
course,
for saying what might happen in future experiments, but not in
interpreting data.
The usual example is the square of the neutrino mass, m^2. If somebody
thinks the measured value should be positive, she will be sadly misled.
If she says that m^2 < 0.5 eV^2 at the 90% CL based on either Bayesian or
frequentists arguments, then there's a useful limit to use in designing
future experiments. But in using that result, the experimental number m^2
= 0.10 +/- 0.15 eV^2 (or whatever it is) must be used.
The halfway house is to think of the experimental distribution of E(B-V)
as the physical E*(B-V) distribution convoluted with the experimental
resolution. But kicking out negative results is dangerous nonsense.
Praises be to Neyman...
Don
|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|
Don Groom (Particle Data Group, Supernova Cosmology Project)
DEGroom(at)lbl.gov www-ccd.lbl.gov Voice: 510/486-6788 FAX: 510/486-4799
Analog: 50-308//Berkeley Lab//Berkeley, CA 94720
This archive was generated by hypermail 2.1.4 : Thu Feb 27 2003 - 13:01:05 PST