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A low frequency stochastic background of gravitational waves may be detectedby pulsar timing experiments in the next five to ten years. Using methodsdeveloped to analyze interferometric gravitational wave data, in this paper welay out the optimal techniques to detect a background of gravitational wavesusing a pulsar timing array. We show that for pulsar distances andgravitational wave frequencies typical of pulsar timing experiments, neglectingthe effect of the metric perturbation at the pulsar does not result in asignificant deviation from optimality. We discuss methods for setting upperlimits using the optimal statistic, show how to construct skymaps using thepulsar timing array, and consider several issues associated with realisticanalysis of pulsar timing data.

Optimal strategies for gravitational wave stochastic background searches in pulsar timing data