  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.
