Bayesian Inference on EMRI Signals in LISA Data

Abstract

This research activity is concerned with the applications of Bayesian Monte Carlo methods for the detection and parameter estimation of the gravitational wave signals generated by a special type of gravitational wave sources called extreme mass ratio inspirals (EMRIs). EMRIs are considered to be one of the most important potential sources of gravitational waves in space-time, to be observed with the planned Laser Interferometer Space Antenna (LISA). The data analysis of such sources is a challenging statistical and computational problem because of the large parameter space, weak amplitudes of the signals, complicated nature of the underlying waveform model and that of the LISA data. The posterior density surface of EMRI signals is full of local modes and ordinary Monte Carlo samplers usually fail to explore such multi-modal densities. This thesis tackles the problem of the detection and parameter estimation of such sources by establishing a Bayesian framework in which the posterior distribution is explored with the help of advanced Monte Carlo sampling methods such as parallel tempering Markov chain Monte Carlo. The LISA response to the incoming gravitational wave signals is not simple and requires some further manipulations to adjust the measured signals for different dynamics to which LISA will be exposed during its operation. This response is derived in two different ways, i.e. full LISA response and the low frequency approximation. This framework was applied with a great success in different scenarios ranging from the detection and estimation of parameters of a single EMRI source buried in LISA instrument noise to the detection and estimation of parameters of a particular EMRI source from data in which there are multiple EMRI sources contaminated with the instrument noise as well as other gravitational sources of noise. The results show that our Bayesian methodology is indeed capable of facing the challenge of the detection and parameter estimation of the signals from EMRI sources in realistic LISA data.