Beyond diagonal approximations: improved covariance modeling for pulsar timing array data analysis
Standard Pulsar Timing Array (PTA) analysis uses a diagonal covariance approximation in Fourier space, which ignores frequency correlations introduced by finite observation windows and biases spectral parameter estimates. The authors propose an improved method that computes time-domain autocorrelation on a coarse grid, interpolates it accurately, and incorporates it into a low-rank likelihood using the Sherman–Morrison–Woodbury identity. This approach captures frequency correlations faithfully without Gibbs ringing artifacts.