Interpolation Techniques for Mcmc Parameter Estimation on Compact Binary Coalescence Gravitational-wave Signals

With gravitational-wave detection on the horizon, astronomers look for ways of extracting useful information from a detected gravitational wave. Like its electromagnetic cousin, a gravitational wave carries important information about the characteristics of its source, and these characteristics can be recovered through numerical analysis. Using one promising technique known as a Metropolis-Hastings Markov Chain Monte Carlo (MCMC) simulation, astronomers can produce a probability distribution over an entire parameter space describing gravitational wave signals; given the gravitational wave data, the MCMC produces a sequence of parameter samples whose distribution converges to the probability density on parameter space implied by the data. Although an MCMC simulation will produce the equilibrium probability distribution in an infinite amount of time, a simulation that runs for a finite amount of time may not. This work focuses on using a kD-tree sorting structure to improve MCMC sampling. We show that a simple sampling method effectively recovers an accurate probability distribution in two dimensions but performs worse than a non-interpolated run in nine dimensions. We explain how dimensionality issues and correlations between the nine parameters – which are not taken into account by the simple sampling method – can cause the simple sampling method to yield inaccurate distributions, and we compare these results to those from an interpolated MCMC simulation with a more sophisticated sampling method which takes correlation into account. Improving the convergence of an MCMC simulation through interpolation would allow for faster, more frequent analysis of gravitational wave signals as well as higher confidence in recovered probability distributions.