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A new model independent method is presented for the analysis of pulsar timingdata and the estimation of the spectral properties of an isotropicgravitational wave background (GWB). We show that by rephrasing the likelihoodwe are able to eliminate the most costly aspects of computation normallyassociated with this type of data analysis. When applied to the InternationalPulsar Timing Array Mock Data Challenge data sets this results in speedups ofapproximately 2 to 3 orders of magnitude compared to established methods. Wepresent three applications of the new likelihood. In the low signal to noiseregime we sample directly from the power spectrum coefficients of the GWBsignal realization. In the high signal to noise regime, where the data cansupport a large number of coefficients, we sample from the joint probabilitydensity of the power spectrum coefficients for the individual pulsars and theGWB signal realization. Critically in both these cases we need make noassumptions about the form of the power spectrum of the GWB, or the individualpulsars. Finally we present a method for characterizing the spatial correlationbetween pulsars on the sky, making no assumptions about the form of thatcorrelation, and therefore providing the only truly general Bayesian method ofconfirming a GWB detection from pulsar timing data.

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