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

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). Taking a Bayesian approach, 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 2-3 orders of magnitude compared to established methods, in the most extreme cases reducing the run time from several hours on the high performance computer DARWIN'' to less than a minute on a normal work station. Because of the versatility of this approach, 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 using a guided Hamiltonian sampler'' to sample efficiently from this high-dimensional (similar to 1000) space. 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 show that, if desired, a power-law model can still be fitted during sampling. We then apply this method to a more complex data set designed to represent better a future International Pulsar Timing Array or European Pulsar Timing Array data release. We show that even in challenging cases where the data features large jumps of the order 5 years, with observations spanning between 4 and 18 years for different pulsars and including steep red noise processes we are able to parametrize the underlying GWB signal correctly. 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.