  Since the very first detection of gravitational waves from the coalescence of
two black holes in 2015, Bayesian statistical methods have been routinely
applied by LIGO and Virgo to extract the signal out of noisy interferometric
measurements, obtain point estimates of the physical parameters responsible for
producing the signal, and rigorously quantify their uncertainties. Different
computational techniques have been devised depending on the source of the
gravitational radiation and the gravitational waveform model used. Prominent
sources of gravitational waves are binary black hole or neutron star mergers,
the only objects that have been observed by detectors to date. But also
gravitational waves from core collapse supernovae, rapidly rotating neutron
stars, and the stochastic gravitational wave background are in the sensitivity
band of the ground-based interferometers and expected to be observable in
future observation runs. As nonlinearities of the complex waveforms and the
high-dimensional parameter spaces preclude analytic evaluation of the posterior
distribution, posterior inference for all these sources relies on
computer-intensive simulation techniques such as Markov chain Monte Carlo
methods. A review of state-of-the-art Bayesian statistical parameter estimation
methods will be given for researchers in this cross-disciplinary area of
gravitational wave data analysis.
