Mathematics – Probability
Scientific paper
Oct 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999phdt.........9m&link_type=abstract
Thesis (PhD). THE LOUISIANA STATE UNIVERSITY AND AGRICULTURAL AND MECHANICAL COL., Source DAI-B 60/04, p. 1651, Oct 1999, 135 pa
Mathematics
Probability
2
Bayesian, Allegro
Scientific paper
The first half of this dissertation discusses the details of calibrating a resonant mass gravitational wave antenna and determining its sensitivity. We dispense with the assumption of a perfectly tuned antenna and transducer and model the system using a coordinate rotation. We demonstrate that all of the important model parameters can be directly measured. We demonstrate that the signal response of the two detector modes should be equal despite any mistuning and that the mistuning parameter can be measured in two separate ways. These properties are useful for determining the degree to which a real detector's behavior parallels that of an ideal two-mode system. We compare the predictions of the model to the output of the ALLEGRO system and determine that a resonance in the hardware used to apply calibration signals is the source of an observed 15% difference in signal response. We extend the model to include this additional resonance. The second half of this dissertation discusses the problem of comparing lists of candidate events acquired from different gravitational wave detectors in search of statistically meaningful coincidences. We demonstrate that a Bayesian approach is the most robust method of inferring if signals are present in the data. We use a combination of multinomial and Poisson distributions to form a likelihood function describing the results of any coincidence experiment. We establish a meaningful basis for choosing a prior probability for Bayesian analyses. We show that the results of a Bayesian analysis do not depend arbitrarily on how the data is subdivided. Finally, using the results of the 1991 and 1994 ALLEGRO and EXPLORER runs, we establish an upper limit on the mean rate of detectable gravity wave bursts that is no more than 9 events per year above a dimensionless strain threshold of 2.3 × 10-18.
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