From l.lyons1@physics.ox.ac.uk Wed Mar 14 17:55:45 2007
MIME-Version: 1.0
Content-type: text/plain;
	charset="iso-8859-1"
X-MimeOLE: Produced By Microsoft Exchange V6.5
Content-class: urn:content-classes:message
Subject: Score statistics
Date: Thu, 15 Mar 2007 00:55:40 -0000
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
Thread-Topic: Score statistics
Thread-Index: AcdRan+8UZLCHY2vQXyZAX90WSAnpwAHaGqXAR62G1sAaF0g1ADNxTUVAR9FNdMADtVEqwHBPx7/
From: "Louis Lyons" <l.lyons1@physics.ox.ac.uk>
To: <cohen@slac.stanford.edu>, <jeffrey@cosmic.arc.nasa.gov>,
        <pilla@po.cwru.edu>, <pingw@slac.stanford.edu>,
        <yedmonds@slac.stanford.edu>, <conrad@particle.kth.se>,
        <elliott@slac.stanford.edu>, <jchiang@slac.stanford.edu>,
        <pln@slac.stanford.edu>, <digel@slac.stanford.edu>,
        <kamae@slac.stanford.edu>, <jpnorris@stanford.edu>,
        <echarles@slac.stanford.edu>, <wai@slac.stanford.edu>,
        <htajima@slac.stanford.edu>, <carson@slac.stanford.edu>
Cc: <rice@stat.berkeley.edu>, <bickel@stat.berkeley.edu>
X-PMX-Version: 5.3.0.289146, Antispam-Engine: 2.5.0.283055, Antispam-Data: 2007.3.14.173934
X-PerlMx-Spam: Gauge=IIIIIII, Probability=7%, Report='SUPERLONG_LINE 0.05, __CT 0, __CTE 0, __CTYPE_CHARSET_QUOTED 0, __CT_TEXT_PLAIN 0, __HAS_MSGID 0, __IMS_MSGID 0, __MIME_TEXT_ONLY 0, __MIME_VERSION 0, __SANE_MSGID 0'
X-MIME-Autoconverted: from quoted-printable to 8bit by mailbox.slac.stanford.edu id l2F0tjAq022785

 
Hello GLAST statistics people,

I visited the Berkeley Statistics Department yesterday, and spoke with
John Rice and Peter Bickel. One of the topics that came up was the
"score test" for assessing the significance of a possible signal above
a smooth background. The more usual method we use at present is to
compare the likelihood ratio for the hypotheses H0 ( = background
only) and H1 ( = background + signal). H1 typically will include 3
more parameters, for signal strength A, position and width. Because
the position and width are meaningless when the signal strength is
zero, the likelihood ratio fails to satisfy the conditions for it to
behave like a chi-squared.

The score test T instead makes use of the derivative of the log
likelihood with respect to the signal strength A, evaluated at A=0. It
does require the largest value of T to be found, for varying values of
the signal position and width.

According to John and Peter, the main advantage of the score test is
that it does not require maximisation with respect to A - in the
likelihood ratio approach, finding the amplitude of the largest
statistical fluctuation for data generated under H0 can be tricky (The
score statistic does, however, need the largest value T* with respect
to variations in the signal's position and width). John and Peter do
not regard it as necessary to scale the statistic by some factr
depending on the width or on the number of events. They would also
calculate the distribution of T* by Monte Carlo, rather than relying
on asymptotic theorems.
	 
John and Peter: I hope this is a fair representation of what you
patiently tried to explain to me
	 
Ramani: I would like to call you up some time, to chat about your talk
on this
	 
	                       Best wishes
	                              Louis