Markov chain Monte Carlo methods for Bayesian gravitational radiation data analysis

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Abstract
The LIGO and VIRGO kilometer length laser interferometric gravitational radiation detectors should observe numerous mergers of compact binary systems. The accurate determination of the binary’s signal parameters is a critical task for the observers. Important cosmological information, such as an independent measurement of the Hubble constant, can be derived if an accurate determination of the distance to the event is achieved. A Bayesian approach to the parameter estimation problem has become a popular topic. Unfortunately the multidimensional integrals that are inherent in the calculation of the Bayes estimator can be computationally prohibitive. In this paper we show that computational difficulties can be overcome by using the Gibbs sampler to calculate posterior distributions. The Bayesian approach and its implementation via Markov chain Monte Carlo calculations is illustrated by way of an example involving four parameters.