Variance in PTA Sensitivity Due to Uncertainty in GWB

Pulsar timing sensitivity curves utilize maximum a-posteriori (MAP) estimate for the model parameters of the stochastic gravitational wave background and intrinsic red noise of pulsars. This is an idealization that does not account for the uncertainty in these model parameters. A more realistic adaptation is to randomly draw model parameter samples and see how much the sensitivity varies from the MAP estimate. This can be performed efficiently using the Rank-Reduced Formalism which is derived from the marginalization of the Fourier coefficients in the PTA likelihood function.