Fast Bayesian analysis of individual binaries in pulsar timing array data

TL;DR

This paper presents a novel Bayesian analysis method that significantly speeds up the detection of individual supermassive black hole binaries in pulsar timing array data by efficiently marginalizing nuisance parameters and precomputing key quantities.

Contribution

The authors introduce a new likelihood formulation that accelerates Bayesian analysis by over four orders of magnitude, enabling more complex and large-scale pulsar timing array studies.

Findings

Achieved >10,000x speedup in parameter exploration

Efficient marginalization over nuisance parameters using MCMC

Facilitates analysis of multiple binaries and eccentric orbits

Abstract

Searching for gravitational waves in pulsar timing array data is computationally intensive. The data is unevenly sampled, and the noise is heteroscedastic, necessitating the use of a time-domain likelihood function with attendant expensive matrix operations. The computational cost is exacerbated when searching for individual supermassive black hole binaries, which have a large parameter space due to the additional pulsar distance, phase offset and noise model parameters needed for each pulsar. We introduce a new formulation of the likelihood function which can be used to make the Bayesian analysis significantly faster. We divide the parameters into projection and shape parameters. We then accelerate the exploration of the projection parameters by more than four orders of magnitude by precomputing the expensive inner products for each set of shape parameters. The projection parameters include nuisance parameters such as the gravitational wave phase offset at each pulsar. In the new scheme, these troublesome nuisance parameters are efficiently marginalized over using multiple-try Markov chain Monte Carlo sampling as part of a Metropolis-within-Gibbs scheme. The acceleration provided by our method will become increasingly important as pulsar timing datasets rapidly grow. Our method also makes sophisticated analyses more tractable, such as searches for multiple binaries, or binaries with non-negligible eccentricities.