Carron, Wolk & Szapudi (2014)

The big idea¶

To do inference you need not only a model but mocks and a covariance. Carron, Wolk & Szapudi give a fast, exact method to simulate a wide class of random fields with a prescribed two-point function on a periodic grid of twice the survey side using FFTs. They show that a finite survey boundary breaks the field’s translation invariance and correlates the observable Fourier modes — the “supersurvey” or “beat-coupling” modes that dominate the power-spectrum covariance on large scales — and that these are accounted for exactly by the non-linear transformations of the Gaussian field. Applied to a real galaxy field (CFHTLS) modelled as Poisson sampling of a lognormal field, the method reproduces power spectra, counts-in-cells distributions, and covariances consistent with the data, and recovers the information plateau seen in SDSS and $N$-body simulations.

Use in progenax¶

• The GRF realization step. progenax builds its field with the same idea — draw Gaussian Fourier amplitudes scaled by $\sqrt{P(k)} = k^{-\beta/2}$ and inverse-FFT (gaussian_random_field) — then apply the monotone copula map. This is the FFT-based, prescribed-spectrum construction of this paper.

• Mock covariances. The realization simulator supplies the mock covariance used (Hartlap-corrected) in the Fisher forecast and the Gaussian-likelihood block; the supersurvey/beat-coupling caveat is the reason the analytic Gaussian band-power covariance underestimates the true mock covariance for the non-Gaussian log-density field — a finding the Differentiable inference — natal cloud parameters from cluster substructure layer guards against by using the mock covariance.

Notes¶

• Part of the Szapudi-group lineage with Coles & Jones (1991), Szapudi & Pan (2004), Carron & Szapudi (2013), Carron & Szapudi (2014); the realization here is the practical companion to that theory.

• progenax differs in target marginal: the FDF imposes the BM19 lognormal + power-law marginal via a rank copula, not a pure lognormal.