SEMINARS
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Spring 2005
PHYSICS SEMINAR
Friday, February 25, 2005
12:30—Room 221 (Miller Room), Rockefeller
Ramani S. Pilla
Department of Statistics and Department of Biology, CASE
A geometric approach to distinguish between a new source and random
fluctuations: Applications to High Energy Physics
One of the fundamental problems in the analysis of experimental data
is determining the statistical significance of a putative signal. Such
aproblem can be cast in terms of classical "hypothesis testing", where
a null hypothesis describes the background and an alternative hypothesis
characterizes the signal as a perturbation of the background. This
testing problem is often addressed by a chi-square goodness-of-fit or a
likelihood ratio test (LRT) statistic. In
general, the former does not yield good power in detecting the signal
and the latter has lacked an analytically tractable reference
distribution required to calibrate a test statistic. Pilla and Loader
have introduced a new test statistic based on perturbation theory to
detect the presence of a signal. We review its reference distribution,
which has an elegant geometrical interpretation and broad applicability,
and note the connection with the LRT. We illustrate the technique in
the context of a model problem from particle physics: the search for a
new particle resonance. Monte Carlo results demonstrate that the
proposed score test is significantly more powerful, resulting in a
higher rate of signal detection when a signal is present in the data.
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