Synthetic demo: FLI vs 3×2pt

This repository ships a fast, CPU-only synthetic baseline to compare field-level inference (FLI) with a compressed 3×2pt-like analysis on the same toy dataset. It runs in seconds on a laptop and serves as an executable blueprint for the real analysis.

What it does - Generates flat-sky 2D maps on an nx × ny grid: - Underlying Gaussian matter overdensity δ with a smooth toy power shape P0(k). - Galaxy overdensity g = b·δ + n_g (white Gaussian pixel noise). - Shear E-mode γ_E = 0.5·δ + n_γ (white Gaussian pixel noise). - Runs two inference paths for parameters (A, b): - FLI: exact per-mode complex-Gaussian likelihood in Fourier space, marginalizing the latent field analytically (diagonal in k for a periodic box). - 3×2pt: binned FFT power spectra P_gg, P_gE, P_EE with a diagonal Gaussian likelihood using per-bin sample variances. - Plots both posteriors together and marks the truth.

Quick start - Install and test (see Getting Started page), then run:

python scripts/run_synthetic_comparison.py --config configs/demo.yaml

Outputs - figures/synthetic_constraints.png: 2D contours (68/95%) and 1D marginals for A and b, overlaying FLI (C0) and 3×2pt (C1). - Console logs with ML estimates for (A, b) for both methods.

Notes - The model is intentionally simple, but the wiring mirrors the real pipeline: shared latent field, correlated observables, clear forward model, and apples-to-apples comparison between full-mode and compressed summaries. - The amplitude A is an effective parameter (not calibrated to σ8). The comparison focuses on constraint sizes and relative performance, not cosmological realism.