sys_mapping

Inference of multiplicative and additive systematics in galaxy density maps.

User guide

• Overview
  • Galaxy clustering and the role of systematics
  • Notation and conventions
  • The observed galaxy overdensity
  • Systematic template maps
  • Contamination model
  • Gaussian log-likelihood (Eq. 17)
  • Skew-normal log-likelihood (Eq. 18)
  • Template PCA rotation (Appendix A)
  • Noise debiasing (Eq. 21)
  • Two-point function correction (Eq. 15–16)
  • Model selection (Eq. 19)
  • Per-galaxy systematic weights
  • Summary of the workflow
  • Analysis execution pipeline
• Installation
  • Requirements
  • From PyPI
  • Create the environment
  • Install in editable mode
  • Run the test suite
  • Build the documentation
• Quickstart
  • Methods overview
  • Step 1 — Generate systematic template maps
  • Step 2 — Simulate the galaxy field and inject contamination
  • Step 3 — Compute the observed overdensity
  • Step 4 — PCA rotation of templates
  • Step 5 — Run all decontamination methods
  • Step 6 — MCMC diagnostics: extract MAP estimates
  • Step 7 — Likelihood ratio test
  • Step 8 — Two-point function correction
  • Expected output summary
  • Results on 100 mock realisations

Methods & references

• Methods Reference
  • Core contamination model
  • Gaussian and skew-normal likelihood
  • MCMC inference
  • Template PCA rotation
  • Noise debiasing
  • Two-point function correction
  • Likelihood ratio test (model selection)
  • Pseudo-\(C_\ell\) power spectrum
  • Block bootstrap covariance
  • Jack-knife covariance
  • ElasticNet regression
  • Iterative Systematics Decontamination (ISD)
  • Null tests and SNR ranking
  • Mock catalog generation
  • HEALPix map utilities
  • Two-point function measurement
  • Method comparison table
• Bibliography
  • Ross et al. 2011
  • Ho et al. 2012
  • Elsner, Leistedt & Peiris 2016
  • Leistedt & Peiris 2014
  • Elsner, Leistedt & Peiris 2017
  • Weaverdyck & Huterer 2021
  • Rezaie et al. 2020
  • Alonso et al. 2019 — NaMaster
  • Berlfein, Mandelbaum & Schafer 2024
  • Rodríguez-Monroy et al. 2025
  • Cornish et al. 2026
  • Tanidis et al. 2026

Validation & tests

• Testing
  • Running the tests
  • Test modules
  • Test design philosophy
  • Continuous integration
  • Systematic test matrix
  • Timing scaling tests
  • Adding new tests
  • Real-template integration tests
• Analysis of 100 mocks
  • Run configuration
  • Mock generation
  • Systematic templates
  • Parameter recovery — all six methods
  • Likelihood ratio test: additive vs. combined model
  • Multiplicative parameter recovery (MCMC-comb)
  • Scatter parameter recovery
  • Output files
• Model test matrix
  • Configuration
  • Tier 1 — single contamination type
  • Tier 2 — mixed additive + multiplicative
  • Compute time
  • Histograms
  • Reproducing the results
• End-to-end validation
  • Simulation Setup
  • Contamination Scenarios
  • Methods Under Test
  • Galaxy Maps
  • Overdensity Distributions
  • Scatter Plots: Recovered vs. True Field
  • Weight Maps
  • Recovery Metrics
  • Amplitude Recovery
  • Null Tests
  • Template SNR Ranking
  • Interpretation and Recommendations
• Progressive Template Contamination Study
  • Motivation
  • Experimental design
  • Template localisation — S/N per template
  • LRT model selection
  • Detection performance
  • Summary table
  • Reproduction
• Real-template single-mock validation
  • Mock configuration
  • Method recovery
  • Results (5 mocks, NSIDE = 64)
  • Model selection and diagnostics
  • Running the validation
  • Outcome
• Simulation tests: GLASS and Uchuu mocks with LSDR10 systematics
  • Mock catalogs
  • Systematic template maps
  • Contamination injection
  • w(θ) recovery results
  • Recovery metric summary
  • Contamination parameter recovery
  • Discussion
  • How to reproduce
  • References

Application to real data: Legacy Survey DR10

• Running the real-data pipeline
  • Input data
  • Running the pipeline
  • Output files
• Results: systematic weights
  • Run configuration
  • Sample overview
  • Systematics are detected: Likelihood Ratio Test
  • Fractional systematic uncertainty on \(w(\theta)\)
  • Is LS10 BGS (\(r < 19.5\)) systematics-limited?
  • Cross-sample comparison (NSIDE 64)
  • Per-sample results — all 9 samples
  • MAP parameters — 11-template analysis (NSIDE 64)
  • Outcome
• LS10 systematic-correction recommendations
  • Decision framework
  • Recommended weight and resolution per sample
  • σ̂_comb goodness-of-fit across resolutions
  • Systematic uncertainty budget
  • Per-sample angular correction profiles
  • Caveats and limitations
• BGS VLIM log M_* ≥ 9.0, z < 0.08 — detailed systematic analysis
  • Sample statistics
  • Goodness-of-fit: \(\hat{\sigma}\) by method and resolution
  • Likelihood Ratio Test (additive vs combined model)
  • Template amplitude ranking — additive model (MCMC-add, NSIDE 64)
  • Template amplitude ranking — multiplicative model (MCMC-comb, NSIDE 64)
  • Per-galaxy weight statistics (NSIDE 64)
  • Systematic weight maps
  • Systematic weight distributions
  • Angular clustering w(θ) before and after correction
  • Cosmological analysis verdict
• BGS VLIM log M_* ≥ 9.5, z < 0.12 — detailed systematic analysis
  • Sample statistics
  • Goodness-of-fit: \(\hat{\sigma}\) by method and resolution
  • Likelihood Ratio Test (additive vs combined model)
  • Template amplitude ranking — additive model (MCMC-add, NSIDE 64)
  • Template amplitude ranking — multiplicative model (MCMC-comb, NSIDE 64)
  • Per-galaxy weight statistics (NSIDE 64)
  • Systematic weight maps
  • Systematic weight distributions
  • Angular clustering w(θ) before and after correction
  • Cosmological analysis verdict
• BGS VLIM log M_* ≥ 10.0, z < 0.18 — detailed systematic analysis
  • Sample statistics
  • Goodness-of-fit: \(\hat{\sigma}\) by method and resolution
  • Likelihood Ratio Test (additive vs combined model)
  • Template amplitude ranking — additive model (MCMC-add, NSIDE 64)
  • Template amplitude ranking — multiplicative model (MCMC-comb, NSIDE 64)
  • Per-galaxy weight statistics (NSIDE 64)
  • Systematic weight maps
  • Systematic weight distributions
  • Angular clustering w(θ) before and after correction
  • Cosmological analysis verdict
• BGS VLIM log M_* ≥ 10.25, z < 0.22 — detailed systematic analysis
  • Sample statistics
  • Goodness-of-fit: \(\hat{\sigma}\) by method and resolution
  • Likelihood Ratio Test (additive vs combined model)
  • Template amplitude ranking — additive model (MCMC-add, NSIDE 64)
  • Template amplitude ranking — multiplicative model (MCMC-comb, NSIDE 64)
  • Per-galaxy weight statistics (NSIDE 64)
  • Systematic weight maps
  • Systematic weight distributions
  • Angular clustering w(θ) before and after correction
  • Cosmological analysis verdict
• BGS VLIM log M_* ≥ 10.5, z < 0.26 — detailed systematic analysis
  • Sample statistics
  • Goodness-of-fit: \(\hat{\sigma}\) by method and resolution
  • Likelihood Ratio Test (additive vs combined model)
  • Template amplitude ranking — additive model (MCMC-add, NSIDE 64)
  • Template amplitude ranking — multiplicative model (MCMC-comb, NSIDE 64)
  • Per-galaxy weight statistics (NSIDE 64)
  • Systematic weight maps
  • Systematic weight distributions
  • Angular clustering w(θ) before and after correction
  • Cosmological analysis verdict
• BGS VLIM log M_* ≥ 10.75, z < 0.31 — detailed systematic analysis
  • Sample statistics
  • Goodness-of-fit: \(\hat{\sigma}\) by method and resolution
  • Likelihood Ratio Test (additive vs combined model)
  • Template amplitude ranking — additive model (MCMC-add, NSIDE 64)
  • Template amplitude ranking — multiplicative model (MCMC-comb, NSIDE 64)
  • Per-galaxy weight statistics (NSIDE 64)
  • Systematic weight maps
  • Systematic weight distributions
  • Angular clustering w(θ) before and after correction
  • Cosmological analysis verdict
• BGS VLIM log M_* ≥ 11.0, z < 0.35 — detailed systematic analysis
  • Sample statistics
  • Goodness-of-fit: \(\hat{\sigma}\) by method and resolution
  • Likelihood Ratio Test (additive vs combined model)
  • Template amplitude ranking — additive model (MCMC-add, NSIDE 64)
  • Template amplitude ranking — multiplicative model (MCMC-comb, NSIDE 64)
  • Per-galaxy weight statistics (NSIDE 64)
  • Systematic weight maps
  • Systematic weight distributions
  • Angular clustering w(θ) before and after correction
  • Cosmological analysis verdict
• BGS VLIM log M_* ≥ 11.25, z < 0.35 — detailed systematic analysis
  • Sample statistics
  • Goodness-of-fit: \(\hat{\sigma}\) by method and resolution
  • Likelihood Ratio Test (additive vs combined model)
  • Template amplitude ranking — additive model (MCMC-add, NSIDE 64)
  • Template amplitude ranking — multiplicative model (MCMC-comb, NSIDE 64)
  • Per-galaxy weight statistics (NSIDE 64)
  • Systematic weight maps
  • Systematic weight distributions
  • Angular clustering w(θ) before and after correction
  • Cosmological analysis verdict
• BGS VLIM log M_* ≥ 11.5, z < 0.35 — detailed systematic analysis
  • Sample statistics
  • Goodness-of-fit: \(\hat{\sigma}\) by method and resolution
  • Likelihood Ratio Test (additive vs combined model)
  • Template amplitude ranking — additive model (MCMC-add, NSIDE 64)
  • Template amplitude ranking — multiplicative model (MCMC-comb, NSIDE 64)
  • Per-galaxy weight statistics (NSIDE 64)
  • Systematic weight maps
  • Systematic weight distributions
  • Angular clustering w(θ) before and after correction
  • Cosmological analysis verdict

API reference

• sys_mapping.contamination
  • n_free_params()
  • pack_params()
  • unpack_params()
  • apply_contamination()
  • invert_contamination()
  • compute_two_point_correction()
• sys_mapping.likelihood
  • make_log_likelihood()
• sys_mapping.maps
  • Synthetic template families
  • Real observational templates
• sys_mapping.inference
  • GPU / vectorised mode
  • make_log_prob()
  • run_mcmc()
  • get_mle_params()
  • get_param_variance_from_chain()
  • get_param_covariance_from_chain()
• sys_mapping.correction
  • debias_params()
  • rotate_templates()
  • transform_params_from_rotated()
  • correct_two_point_function()
  • correct_power_spectrum_harmonic()
• sys_mapping.model_selection
  • LikelihoodRatioResult
  • likelihood_ratio_test()
• sys_mapping.bootstrap
  • block_bootstrap_variance()
  • jackknife_covariance()
• sys_mapping.utils
  • compute_covariance_matrix()
  • compute_amplitude_bias()
  • measure_two_point_function()
  • measure_two_point_function_corrfunc()
  • measure_kk_correlation_treecorr()
  • measure_kk_correlation_corrfunc()
• sys_mapping.power_spectrum
  • measure_pseudo_cl()
  • subtract_template_cl()
  • harmonic_bias()
  • mode_projection_bias()
• sys_mapping.regression
  • elasticnet_contamination_fit()
  • iterative_systematics_decontamination()
  • method_comparison()
  • run_decontamination()
• sys_mapping.diagnostics
  • null_test_cross_correlations()
  • snr_template_ranking()
  • footprint_mask_diagnostics()
• sys_mapping.mocks
  • Contamination scenarios
  • Galaxy field model
  • MockCatalog
  • generate_lognormal_field()
  • make_galactic_mask()
  • make_mock_catalog()
  • make_mock_suite()
• sys_mapping.glass_mocks
  • Workflow
  • MockCatalogDict
  • measure_nz()
  • generate_glass_fullsky_mock()
• sys_mapping.simulation
  • Contamination injection strategy
  • ContaminationConfig
  • make_contamination_grid()
  • load_uchuu_mock()
  • load_systematic_maps()
  • apply_footprint_mask()
  • inject_systematics()
  • save_simulation_catalog()
  • load_simulation_catalog()
  • run_wtheta_recovery()

Development

• Changelog