Abstract:
This work addresses the exploration of Bayesian MCMC methods applied to
problems in gravitational wave physics. The thesis consists of two parts. In
the first part a Bayesian Markov chain Monte Carlo technique is presented
for estimating the astrophysical parameters of gravitational radiation signals
from a neutron star in laser interferometer data. This computational algorithm
can estimate up to six unknown parameters of the target, including
the rotation frequency and frequency derivative, using reparametrization, delayed
rejection and Metropolis-Coupled Markov Chain Monte Carlo. Results
will be given for different synthesized data sets in order to demonstrate the
algorithm’s behaviour for different observation lengths and signal-to-noise
ratios. The probability of detecting weak signals is assessed by a model comparison,
based on the BIC, between a model that postulates a signal and one
that postulates solely noise within the data.
The second part of the thesis adresses the tremendous data analysis challenges
for the Laser Interferometer Space Antenna (LISA) with the need to
account for a large number of gravitational wave signals from compact binary
systems expected to be present in the data. The basis of a Bayesian
method is introduced that can address this challenge, and its effectiveness
is demonstrated on a simplified problem involving one hundred synthetic sinusoidal
signals in noise. The reversible jump Markov chain Monte Carlo
technique is deployed to infer simultaneously the number of signals present,
the parameters of each identified signal, and the noise level. This approach
is specifically focused on the detection of a large number of sinusoids with
separation of sinusoids that are close in frequency. A robust post-processing
technique handles the label switching problem by a frequency interval separation technique with a subsequent classification according to a mixed model
approximation. The algorithm therefore tackles the detection and parameter
estimation problems simultaneously, without the need to evaluate formal
model selection criteria, such as the Akaike Information Criterion or explicit
Bayes factors. The method produces results which compare very favorably
with classical spectral techniques.