Abstract

This work concerns Bayesian detection statistics in targeted searches for continuous gravitational waves (GWs). The parameter space for continuous GWs can be divided into 2 groups: amplitude parameters which control the signal strength and phase-evolution parameters which determine its time evolution. A common issue in these searches is dealing with these amplitude parameters which do not affect the phase evolution of the system. The F-statistic maximizes the likelihood function of the data analytically over these parameters, while the B-statistic marginalizes over them. The B-statistic, while potentially more powerful and capable of incorporating astrophysical priors, is not used because of the computational difficulty of performing the marginalization. Here we present an approximation to the B-statistic obtained via a Taylor expansion of the marginalization integrand in powers of two of the smaller components of the amplitude metric. We show that our approximation is valid both in the asymptotic limits of the parameters as well as for specific choices of prior distributions. In addition, we use Monte Carlo simulations to show that our approximation is comparable to the exact B-statistic and gives similar detection probabilities.

Library of Congress Subject Headings

Gravitational waves--Mathematical models; Bayesian statistical decision theory

Publication Date

1-2018

Document Type

Thesis

Student Type

Graduate

Degree Name

Astrophysical Sciences and Technology (MS)

Department, Program, or Center

School of Physics and Astronomy (COS)

Advisor

Michael Richmond

Advisor/Committee Member

Richard O'Shaughnessy

Advisor/Committee Member

John T. Whelan

Campus

RIT – Main Campus

Plan Codes

ASTP-MS

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