Speaker
Description
Fisher-matrix forecasts are the standard tool for comparing proposed gravitational-wave detector networks, such as the triangular and double-L designs of the Einstein Telescope. When the likelihood is nearly flat in some direction and only the prior constrains it, the Fisher interval overstates the uncertainty — and because the size of this bias depends on detector geometry, it need not cancel when two networks are compared. I will present the prior-whitened Fisher spectrum: the generalized eigenvalues of the Fisher matrix measured against the prior precision. Each eigenvalue fixes exactly how much the likelihood-only width is inflated relative to the prior-informed one, identifying prior-dominated modes before any posterior sampling. Combined with checks on location, prior–likelihood conflict and likelihood curvature, it tests whether the Gaussian picture behind a Fisher comparison holds. Applied to eight reference networks, the triangular Einstein Telescope is more prior-dominated than the double-L design for 99.5% of 2770 jointly detected binary neutron stars, with a median worst-mode inflation factor of 87 against 7.6 (a comparison of Gaussian-equivalent diagnostics, not of true posterior widths). For binary black holes relocated to a signal-to-noise ratio of 200, at most 7% of sources violate the spectral conditions, yet the curvature condition still fails for 96–99% of sources: a high signal-to-noise ratio alone does not make a Fisher forecast valid. None of these checks requires posterior sampling, so they can screen a forecast before it is trusted.