Bayesian Strategies for Gravitational Radiation Data Analysis
Abstract (Summary)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.
Advisor:Dr. Renate Meyer; Dr. Nelson Christensen
School Location:New Zealand
Source Type:Master's Thesis
Date of Publication:01/01/2006