20,007 research outputs found
Upper Limits from Counting Experiments with Multiple Pipelines
In counting experiments, one can set an upper limit on the rate of a Poisson
process based on a count of the number of events observed due to the process.
In some experiments, one makes several counts of the number of events, using
different instruments, different event detection algorithms, or observations
over multiple time intervals. We demonstrate how to generalize the classical
frequentist upper limit calculation to the case where multiple counts of events
are made over one or more time intervals using several (not necessarily
independent) procedures. We show how different choices of the rank ordering of
possible outcomes in the space of counts correspond to applying different
levels of significance to the various measurements. We propose an ordering that
is matched to the sensitivity of the different measurement procedures and show
that in typical cases it gives stronger upper limits than other choices. As an
example, we show how this method can be applied to searches for
gravitational-wave bursts, where multiple burst-detection algorithms analyse
the same data set, and demonstrate how a single combined upper limit can be set
on the gravitational-wave burst rate.Comment: 26 pages (CQG style), 8 figures. Added study of robustness of limits
Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox
Parrondo's games manifest the apparent paradox where losing strategies can be
combined to win and have generated significant multidisciplinary interest in
the literature. Here we review two recent approaches, based on the
Fokker-Planck equation, that rigorously establish the connection between
Parrondo's games and a physical model known as the flashing Brownian ratchet.
This gives rise to a new set of Parrondo's games, of which the original games
are a special case. For the first time, we perform a complete analysis of the
new games via a discrete-time Markov chain (DTMC) analysis, producing winning
rate equations and an exploration of the parameter space where the paradoxical
behaviour occurs.Comment: 17 pages, 5 figure
A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo (vol 908, 218, 2021)
The Loudest Event Statistic: General Formulation, Properties and Applications
The use of the loudest observed event to generate statistical statements
about rate and strength has become standard in searches for gravitational waves
from compact binaries and pulsars. The Bayesian formulation of the method is
generalized in this paper to allow for uncertainties both in the background
estimate and in the properties of the population being constrained. The method
is also extended to allow rate interval construction. Finally, it is shown how
to combine the results from multiple experiments and a comparison is drawn
between the upper limit obtained in a single search and the upper limit
obtained by combining the results of two experiments each of half the original
duration. To illustrate this, we look at an example case, motivated by the
search for gravitational waves from binary inspiral.Comment: 11 pages, 8 figure
Search For Transient Gravitational Waves In Coincidence With Short-Duration Radio Transients During 2007–2013
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