A Hamiltonian MonteCarlo method for Bayesian inference of supermassive black hole binaries
Abstract
We investigate the use of a Hamiltonian MonteCarlo to map out the posterior density function for supermassive black hole binaries. While previous Markov Chain MonteCarlo (MCMC) methods, such as MetropolisHastings MCMC, have been successfully employed for a number of different gravitational wave sources, these methods are essentially random walk algorithms. The Hamiltonian MonteCarlo treats the inverse likelihood surface as a 'gravitational potential' and by introducing canonical positions and momenta, dynamically evolves the Markov chain by solving Hamiltonʼs equations of motion. This method is not as widely used as other MCMC algorithms due to the necessity of calculating gradients of the loglikelihood, which for most applications results in a bottleneck that makes the algorithm computationally prohibitive. We circumvent this problem by using accepted initial phasespace trajectory points to analytically fit for each of the individual gradients. Eliminating the waveform generation needed for the numerical derivatives reduces the total number of required templates for a ${{10}^{6}}$ 10 6 iteration chain from $\sim {{10}^{9}}$ ~ 10 9 to $\sim {{10}^{6}}$ ~ 10 6 . The result is in an implementation of the Hamiltonian MonteCarlo that is faster, and more efficient by a factor of approximately the dimension of the parameter space, than a Hessian MCMC.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 July 2014
 DOI:
 10.1088/02649381/31/14/145004
 arXiv:
 arXiv:1311.7539
 Bibcode:
 2014CQGra..31n5004P
 Keywords:

 Hamiltonian Monte Carlo;
 supermassive black holes;
 Bayesian inference;
 gravitational waves;
 04.30.w;
 04.30.Db;
 02.50.Ga;
 General Relativity and Quantum Cosmology
 EPrint:
 16 pages, 8 figures