Inferring a binary from a detector network

For detector $k$, model the calibrated data as $d_k(t)=h_k(t;\theta )+n_k(t)$, with a shared source parameter vector $\theta$, separate detector responses, propagation delays and noise $n_k$. Under an independent stationary Gaussian process approximation with one-sided power spectral density $S_k(f)$, define the noise-weighted inner product and likelihood functionStrain power spectral density has units ${\mathrm{Hz}}^{-1}$; the displayed inner product is dimensionless when the Fourier transform integrates over seconds. A matched filter rewards agreement over the full evolving wave phase, weighting frequency bands by their noise. One conspicuous peak is insufficient: a candidate should also have the right distribution of signal across frequency bands and compatible projections in the network.

The parameter paper used coherent Bayesian inference, numerical relativity-informed inspiral–merger–ringdown models and explicit calibration uncertainties. It found a strong distance–inclination correlation; source-frame masses additionally require converting the detector-frame masses by a cosmological redshift.^[ref] Conceptually, multiply the likelihood function by a prior distribution to obtain a posterior distribution. Changes in waveform families, residual structure after subtraction, and checks with a generic transient reconstruction test parts of the modeling assumptions. Detection significance and parameter uncertainty answer different questions.