Likelihood validation

Scope

This validation compares the Fisher forecasts produced by CosmicJellyfish with posterior samples from its Nautilus likelihood interface. It is intentionally a focused integration test rather than a claim that every likelihood, configuration, or cosmological model has been validated.

The recorded run uses the symbolic backend, flat LCDM, Euclid ISTF pessimistic photometric and spectroscopic specifications, and the free cosmological parameters Omegam and sigma8. All nuisance parameters automatically added by the corresponding Fisher calculation were sampled: three intrinsic-alignment parameters for WL and four galaxy-bias plus four shot-noise parameters for GCsp. Thus the Nautilus posteriors and Fisher contours are both marginalised over the same nuisance parameter sets.

The run used 64 Nautilus workers, n_live=500, and n_eff=2000. The tracked summary statistics live in scripts/likelihood_validation_results/wl_gcsp_symbolic_euclid_64cpu_statistics.json. The raw chains and checkpoints are intentionally excluded from the repository.

Results

The figures were generated with CosmicJellyfish’s ChainConsumer integration from the weighted Nautilus chains. Each probe has a stable color pair: dark contours are marginal Fisher forecasts and lighter contours are Nautilus posterior samples. WL is blue, GCsp is green, and the joint result is orange. Dashed lines mark the fiducial cosmology.

Weak lensing

Spectroscopic galaxy clustering

Joint WL + GCsp

This overview shows all six contours: the WL, GCsp, and joint Fisher-Nautilus pairs.

Probe	Nautilus / Fisher: sigma(Omegam)	Nautilus / Fisher: sigma(sigma8)	Correlation: Nautilus / Fisher
WL	1.044	1.048	-0.9930 / -0.9932
GCsp	1.004	1.003	+0.4961 / +0.5083
WL + GCsp	1.013	1.005	-0.8546 / -0.8501

The posterior means are within 0.09 standard deviations of the fiducial for WL, 0.02 for GCsp, and 0.06 for the joint case. Within the sampling precision of the retained chains, this validates the tested WL, GCsp, and joint wedge likelihood implementations against their corresponding marginal Fisher forecasts.

Computational resources

Each probe was submitted as an independent Slurm job with CPUS_PER_TASK=64. The case runner passed all 64 allocated CPUs to Nautilus as multiprocessing workers and pinned OpenMP, BLAS, and NumExpr thread counts to one, avoiding oversubscription inside each worker.

Case	Sampled dimensions	Nautilus workers	n_live	Target n_eff	Recorded elapsed time	Chain ESS
WL	5	64	500	2000	17 min 03 s	2101
GCsp	10	64	500	2000	22 min 29 s	2764
WL + GCsp	13	64	500	2000	1 h 45 min 05 s	2057

Elapsed times include Fisher setup and Nautilus sampling; the latter dominates each case. The three jobs ran concurrently, so their times must not be summed as sequential wall time. The joint case sets the approximately 1 h 45 min validation makespan.

The metadata does not identify the exact JURECA node class. Consult the JURECA DC hardware configuration and Slurm accounting records for node-specific hardware details.

Reproduction

Run the three independent Slurm cases and their dependent post-processing job:

RUN_DIR=/scratch/$USER/cfp/wl-gcsp-64cpu \
N_LIVE=500 N_EFF=2000 CPUS_PER_TASK=64 \
scripts/hpc/slurm/submit_wl_gcsp_nautilus.sh

After copying a completed run locally, regenerate the tracked evidence without copying chains into the repository:

uv run python scripts/likelihood/postprocess/render_likelihood_validation.py \
  --run-dir hpc-results/wl-gcsp-64cpu