Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data

TL;DR

This paper introduces a highly efficient, model-independent Bayesian approach for analyzing pulsar timing data to detect and characterize the gravitational wave background, significantly reducing computational costs and avoiding assumptions about spectral forms.

Contribution

It presents a novel likelihood rephrasing that enables rapid, assumption-free spectral analysis and spatial correlation characterization in pulsar timing data.

Findings

Achieved 2-3 orders of magnitude speedup over existing methods.

Successfully applied to mock data for GWB detection and characterization.

Provided a general Bayesian framework for confirming gravitational wave background signals.

Abstract

A new model independent method is presented for the analysis of pulsar timing data and the estimation of the spectral properties of an isotropic gravitational wave background (GWB). We show that by rephrasing the likelihood we are able to eliminate the most costly aspects of computation normally associated with this type of data analysis. When applied to the International Pulsar Timing Array Mock Data Challenge data sets this results in speedups of approximately 2 to 3 orders of magnitude compared to established methods. We present three applications of the new likelihood. In the low signal to noise regime we sample directly from the power spectrum coefficients of the GWB signal realization. In the high signal to noise regime, where the data can support a large number of coefficients, we sample from the joint probability density of the power spectrum coefficients for the individual pulsars and the GWB signal realization. Critically in both these cases we need make no assumptions about the form of the power spectrum of the GWB, or the individual pulsars. Finally we present a method for characterizing the spatial correlation between pulsars on the sky, making no assumptions about the form of that correlation, and therefore providing the only truly general Bayesian method of confirming a GWB detection from pulsar timing data.