Exploring the Capabilities of Gibbs Sampling in Searches for Gravitational Waves in Pulsar Timing Arrays

The sensitivity of pulsar timing arrays (PTAs) to nano-hertz stochastic gravitational waves (SGWs) relies heavily on two factors: the number of pulsars timed and the number of years each timed pulsar is observed for. Currently, the most sensitive PTA experiments observe close to 80 millisecond pulsars with about a dozen of such pulsars observed for twelve to seventeen years. However, alongside the increase in sensitivity to detection of SGWs, the computational cost of noise modeling and parameter estimation also grows significantly as more pulsars are timed. This poses a significant challenge for Bayesian inference as a typical search for a SGW involves a large number of parameters: at the very least twice the number pulsars in the array plus the number of parameters necessary to model the GW signal. As a result, fast and reliable sampling methods such as Gibbs sampling could be of great use in searches for SGWs in PTAs.

Since the Fourier coefficients and the spectrum of each pulsar’s SGW noise have an analytic form for their conditional probability distribution, Gibbs sampling can be implemented to estimate posterior distributions for such parameters. In this presentation, I explore the capabilities of Gibbs sampling in estimation of the spectrum, amplitude, and the underlying shape of the special correlations induced by SGWs within real and simulated PTA data sets. My findings suggest that Gibbs sampling is fully capable of robust estimation of such parameters and can reduce the cost of SGWs analyses significantly.