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Modified
Sun Oct 15 06:23:48 2006 UTC (8 years, 3 months ago) by
brun
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From Christophe Delaere:
new version of TLimit. It implements Tom Junk's solution for a
bias appearing sometimes when introducing systematics.
Bellow is the detailed information.
Following an exchange of mails between Laurent Duflot and Tom Junk,
Tom wrote the following:
"Laurent Duflot has given me an example which showed me I was wrong with
how I reweight s+b pseudoexperiments to get background-only
pseudoexperiments and vice versa. I am sending this along to Alex Read
and Bill Murray in case they might say "Yes, you should have known that
all along, Tom!". It certainly was a surprise to me.
We do "importance sampling" of s+b and b pseudoexperiments and reweight
them to look like the other kind, and the weight factor is the likelihood
ratio, which coincidentally happens to look like our test statistic.
But the test statistic uses central values of s and b so as not to split
outcomes, and the weights for reweighting pseudoexperiments I was using
were the likelihood ratios using systematically varied s and b on each
pseudoexperiment, where I pick smeared values on each pseudoexperiment.
The problem is that this is biased. Pseudoexperiments in the
background-hypothesis distribution that are more signal-like
preferentially have their background expectations systematically varied
upwards. Pseudoexperiments in the s+b distribution that are more
background-like preferentially have their background expectations
systematically varied downwards. These two kinds of outcomes may
populate the same bin of -2lnQ. Reweighting the bg pseudoexperiments
to look like corresponding s+b pseudoexperiments should take into
account that the corresponding backgrounds are different.
I've approximated this by re-fluctuating the signal and the background
on each pseudoexperiment to get an unbiased target distribution. So the
weight ratio is
Ratio = P(pd|s1+b1)/P(pd|b2)
where pd=pseudodata, s1, b1 are a randomly re-fluctuated signal and
background, and b2 is the fluctuated background which gave me that
pseudodata, and this weight should turn a biased background
pseudoexperiment into a representative s+b pseudoexperiment.
The problem I see now is that the s+b pseudoexperiment should also be
biased, but I do not know how to compute this without running a lot of
pseudoexperiments. It also gets tough as the number of variable
systematic errors gets large.
Nonetheless, the approximation above helps make the reweighted quantities
match more their unweighted counterparts in the large-pseudoexperiment
limit.
Revision
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Modified
Tue Jan 27 13:41:53 2004 UTC (10 years, 11 months ago) by
brun
Original Path:
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File length: 1707 byte(s)
Diff to
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From Christophe Delaere:
TLimit has been modified to take into account statistical errors from the MC.
Tutorial limit.C modified accordingly.
In TMultiLayerPerceptron, add the possibilite to export the NN
in Python format.
Corrected a problem with TEventlist when 2 NN are in the same directory.
Update the example mlpHiggs.C
The web page describing this work has also been updated. see:
http://www.fynu.ucl.ac.be/users/c.delaere/MLP/
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