Novel inference methods for gravitational wave astrophysics

Hu, Yiming (2015) Novel inference methods for gravitational wave astrophysics. PhD thesis, University of Glasgow.

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With the development of more and more elegant and sensitive interferometric gravitational wave detectors, we are expecting the first direct detection of gravitational waves in a short time. This triggers huge interest to develop more powerful tools to perform data analysis on these signals, and to develop a good understanding of the analysis so that confident conclu- sions can be made. A further step would be to view into the future, as the first detections will boost the scientific demands for more powerful future generation detectors, which identifies the task of optimising the site of such detectors.

Bayesian Inference plays a vital role in data analysis, and one excellent example that demon- strates its usefulness is its ability to resolve the tension between multiple models using the methodology of Bayesian Model Selection. In this thesis we apply this methodology to the timing data of pulses from the pulsar 1E 2259+586. With a set of different choices for the prior range, a fair and quantitative comparison can be made between two competing models: that of so-called successive anti-glitches and an anti-/normal glitch pair. Our analysis of the data shows a consistent support for the successive anti-glitches model, with a Bayes Factor of ∼ 45, where the uncertainty has been estimated from nested sampling and from multiple runs that are slightly different, but still within a factor of two, showing a general consistency. Simplifying the timing model will only make the Bayes Factor even bigger, while the two event model is overwhelmingly supported over the one event model.

In gravitational wave data analysis, posteriors are generally complicated structures contain- ing multiple modes. A novel algorithm to achieve efficient sampling for multi-modal pos- teriors, known as mixed MCMC, is proposed in this thesis. This enables communication between multiple regions within the parameter space by adopting a novel jump proposal. We present the mixed MCMC algorithm and first apply it to a toy model problem, where the likelihood may be determined theoretically. By comparing the theoretical and empiri- cally sampled values of 2 log(L) for credible regions that correspond to 68.27%, 95.45% and
99.73%, we conclude that for our illustrative model the sampling result of mixed MCMC is consistent with the theoretical prediction with small uncertainty. Since it does not re- quire multiple chains with different temperatures, mixed MCMC can boost the efficiency of sampling by design, compared with (for example) parallel tempering MCMC.

The sampling strategy of mixed MCMC can be helpful for not only Bayesian Inference, but also more general problems like the global optimisation of future generations of Gravita- tional Wave Detectors. As we expect such problem to be intrinsically high dimensional and multi-modal, mixed MCMC is a suitable sampling method, and we develop and apply it in this thesis. Based on our analysis it is concluded that for both a 3-detector-network and a 5-detector-network, Australia hosts the “best” site, in the sense that such site is most flex- ible, i.e. it can be involved in the largest number of detector networks, involving different component sites, that have a high ‘Figure of Merit’.

The work of gravitational wave data analysis leads to the ultimate goal of making a direct detection of gravitational waves, which in turn requires the ability of distinguish astronomi- cal signals from a noisy background, and assess the significance of each gravitational wave ‘trigger’ (i.e. candidate event) appropriately. There are two types of method for estimating significance and these differ by the key distinction of either removing the foreground events from the background estimation or keeping them in the analysis. This thesis presents the results of a Mock Data Challenge (MDC), carried out within the LIGO Scientific Collabo- ration using different data analysis pipelines, designed to investigate these two methods for estimating significance. It contains a variety of background complexity ranging from simple, realistic to complex, and foreground event rate ranging from zero, low, medium and high. Analysis of the MDC results illustrated that generally all methods for determining the sig- nificance agree well with each other, irrespective of the background complexity. However, a discrepancy became apparent between the results for removal or non-removal of foreground events, for events below a significance level of < 10−3. Our results demonstrated that the removal method is an unbiased estimator for the mean of the significance. However, as the most scientifically interesting events are likely to have a very small numerical value for their significance, such method would overestimate that significance for most of the realisations.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: Bayesian; gravitational wave; data analysis; MCMC; nested sampling; model selection; general relativity; mixed MCMC; anti-glitch; global optimisation; significance of gravitational wave event
Subjects: Q Science > QB Astronomy
Q Science > QC Physics
Colleges/Schools: College of Science and Engineering > School of Physics and Astronomy
Supervisor's Name: Hendry, Prof. Martin and Heng, Dr. Ik Siong
Date of Award: 2015
Depositing User: Dr. Yi-Ming Hu
Unique ID: glathesis:2015-6441
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 08 Jun 2015 12:47
Last Modified: 02 May 2018 12:47
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