Markov Chain Monte Carlo (MCMC) and Bayesian Inference for Gravitational Waves

University essay from Lunds universitet/Astronomi

Abstract: The Laser Interferometer Space Antenna (LISA) is a space borne gravitational wave detec- tor set to launch in 2034, with the objective of detecting and studying the Gravitational Waves (GWs) of our universe. So far, ground-based detectors such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) have been successful in detecting GWs, but the limitations of ground based detectors is what makes LISA so special. With three separate space crafts, each 2.5 million kilometers apart, the detector is expected to mea- sure gravitational radiation within the frequency regime of 0.1 mHz to 1 Hz. With LISA, astronomers will be able to determine the type, mass, as well as the energy released by GW sources. From the data measured with LISA, scientists will be able to challenge Einstein’s theory of General Relativity through the lens of gravity, and perhaps uncover vital information about our universe’s past, present and future. As LISA follows an Earth trailing orbit around the Sun, it is expected to detect GWs emitted by numerous sources simultaneously. This results in one single signal that contains the information of all detectable gravitational sources in the universe. In order to study a single source, the development of a mathematical computer model is required to extract the desired information. This thesis implements Bayesian inference with a stochastic sampling algorithm known as Markov Chain Monte Carlo (MCMC) to tackle the multi-dimensional problem and statistically recover the parameters of the GW. In this thesis, we focus on the ecliptic coordinates of the source, which are just two out of the seven parameters of a GW. We found that MCMC was successful in the localisation of the source from a simulated gravitational wave strain. The ecliptic coordinates were recovered with a standard deviation of less than 1 degree. Expanding the program, we were also able to test the effectiveness of MCMC in the presence of multiple waves, and how their amplitude and frequencies a↵ect the algorithms ability to recover the true position. Lastly, we conclude this paper with an alternative suggestion for extracting the parameters using Multinest, as well as comment on additional research.

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