Bibliography ============ Consolidated reference list for all papers cited in ``hod_mod``. Entries are grouped by topic and ordered chronologically within each group to show the progression of the field. .. contents:: :local: :depth: 1 ---- Cosmology and Power Spectra ----------------------------- Foundation papers for the cosmological framework, linear power spectrum computation, and non-linear emulators used in ``hod_mod``. .. [EisensteinHu1998] Eisenstein D.J. & Hu W. 1998, ApJ 496, 605. Fitting formulae for the linear matter power spectrum without CDM (transfer function). `arXiv:astro-ph/9709066 `_ .. [Lewis2002] Lewis A., Challinor A. & Lasenby A. 2000, ApJ 538, 473. CAMB: Code for Anisotropies in the Microwave Background; ``hod_mod`` uses CAMB for linear :math:`P(k)` via ``LinearPowerSpectrum``. `arXiv:astro-ph/9911177 `_ .. [PlanckCollaboration2018] Planck Collaboration 2018, A&A 641, A6. Planck 2018 cosmological parameters (default cosmology in ``hod_mod``). `arXiv:1807.06209 `_ .. [Aletheia2025] Aletheia Collaboration 2025. Non-linear matter power spectrum emulator used via ``NonLinearPowerSpectrum``. `arXiv:2511.13826 `_ ---- Halo Model Framework ----------------------- The halo model provides the theoretical basis for connecting dark matter halos to observed galaxy statistics. These foundational works established the framework implemented in ``hod_mod``. .. [Asgari2023] Marika Asgari, Alexander J. Mead, Catherine Heymans OJAp 6E 39A 2023. The halo model for cosmology: a pedagogical review. `arXiv:2303.08752 `_ .. [SeljakWarren2004] Seljak U. & Warren M.S. 2004, MNRAS 355, 129. First complete halo model predictions for galaxy clustering including scale-dependent bias; established the 1-halo + 2-halo decomposition. `arXiv:astro-ph/0403698 `_ .. [CooraySheth2002] Cooray A. & Sheth R. 2002, Phys. Rep. 372, 1. Definitive review of halo models of large-scale structure; reference for the 1-halo / 2-halo power spectrum decomposition used throughout ``hod_mod``. `arXiv:astro-ph/0206508 `_ ---- Halo Mass Function and Bias ----------------------------- Calibrations of the halo mass function and halo bias, from early analytic approximations through simulation-calibrated fits to modern emulators. .. [PressSchechter1974] Press W.H. & Schechter P. 1974, ApJ 187, 425. Original analytic derivation of the dark matter halo abundance; historical foundation for all subsequent HMF work. .. [ShethTormen1999] Sheth R.K. & Tormen G. 1999, MNRAS 308, 119. Ellipsoidal collapse HMF; improved agreement with N-body simulations over Press-Schechter. `arXiv:astro-ph/9901122 `_ .. [Jenkins2001] Jenkins A. et al. 2001, MNRAS 321, 372. First large N-body calibration of the HMF across multiple cosmologies. `arXiv:astro-ph/0005260 `_ .. [Tinker2008] Tinker J.L. et al. 2008, ApJ 688, 709. Precision calibration of the HMF from N-body simulations across 11 orders of magnitude in mass; default HMF in ``hod_mod`` (``tinker08``). `arXiv:0803.2706 `_ .. [Tinker2010] Tinker J.L. et al. 2010, ApJ 724, 878. Calibration of the large-scale linear halo bias corresponding to the Tinker+2008 HMF; used in the 2-halo term of ``hod_mod``. `arXiv:1001.3162 `_ .. [ChenCSST2025] Chen Z. et al. 2025, Science China: Physics, Mechanics & Astronomy 68, 9513. CEmulator v2.0: Gaussian-Process emulator of halo statistics (HMF, matter power spectrum, halo-matter cross-correlation) for CSST cosmologies spanning :math:`w_0w_a\nu`CDM; ``make_hmf("csst")`` in ``hod_mod``. `ADS `_ .. [ShenAemulus2025] Shen X. et al. 2025, JCAP 2025 (03), 056. Aemulus-ν: Gaussian-Process HMF emulator for massive-neutrino wCDM cosmologies, calibrated on 150 high-resolution N-body simulations for :math:`M \geq 10^{13}\,M_\odot/h`, :math:`z \leq 2`; ``make_hmf("aemulusnu")`` in ``hod_mod``. `arXiv:2410.00913 `_ .. [Nishimichi2019] Nishimichi T. et al. 2019, ApJ 884, 29. Dark Emulator: Gaussian Process emulation of halo clustering statistics; enables rapid HOD predictions for arbitrary ΛCDM cosmologies. `arXiv:1811.09504 `_ ---- Halo Profiles and Concentration --------------------------------- From the original NFW profile through concentration calibrations to the projected surface-mass-density formulas used in lensing predictions. .. [NFW1997] Navarro J.F., Frenk C.S. & White S.D.M. 1997, ApJ 490, 493. Universal NFW density profile from hierarchical clustering simulations; the default halo profile in ``hod_mod``. `arXiv:astro-ph/9611107 `_ .. [Einasto1965] Einasto J. 1965, Trudy Astrofizicheskogo Instituta Alma-Ata 5, 87. Einasto profile; alternative to NFW available in ``hod_mod``. .. [WrightBrainerd2000] Wright C.O. & Brainerd T.G. 2000, ApJ 534, 34. Analytical formulas for weak-lensing shear and convergence of NFW halos; basis for :math:`\Delta\Sigma(R)` computations in ``hod_mod``. `arXiv:astro-ph/9908213 `_ .. [BryanNorman1998] Bryan G.L. & Norman M.L. 1998, ApJ 495, 80. Virial overdensity :math:`\Delta_{\rm vir}(z)` fitting formula used in halo mass–concentration conversions. `arXiv:astro-ph/9710107 `_ .. [DiemerJoyce2019] Diemer B. & Joyce M. 2019, ApJ 871, 168. Accurate physical model for halo concentrations; default concentration–mass relation in ``hod_mod`` via colossus (``diemer19``). `arXiv:1809.07326 `_ ---- HOD Models ----------- The halo occupation distribution (HOD) connects galaxies to dark matter halos. These references cover the foundational formalism through the models implemented in ``hod_mod/connection/hod/``. .. [BerlindWeinberg2002] Berlind A.A. & Weinberg D.H. 2002, ApJ 575, 587. Foundational HOD formalism paper; introduced the conditional probability of finding :math:`N` galaxies in a halo of mass :math:`M` as the core statistic. `arXiv:astro-ph/0109001 `_ .. [Zheng2005] Zheng Z. et al. 2005, ApJ 633, 791. HOD models with explicit separation of central and satellite galaxies; introduced the :math:`\langle N_{\rm cen}\rangle + \langle N_{\rm sat}\rangle` decomposition that underlies all modern HOD codes. `arXiv:astro-ph/0408564 `_ .. [Zheng2007] Zheng Z. et al. 2007, ApJ 667, 760. HOD fits to DEEP2 and SDSS galaxy samples across redshifts; the parametrization ``HODModel`` in ``hod_mod`` follows Zheng+2007. `arXiv:astro-ph/0703457 `_ .. [More2015] More S. et al. 2015, ApJ 806, 2. HOD analysis of BOSS CMASS using :math:`w_p + \Delta\Sigma`; introduced the incompleteness correction and :math:`\kappa` satellite cut. Reference model for ``MoreHODModel`` in ``hod_mod``. `arXiv:1407.1856 `_ .. [vanUitert2016] van Uitert E. et al. 2016, MNRAS 459, 3251. HOD fits using a Gaussian conditional stellar mass function; reference for ``VanUitert16CSMFModel`` in ``hod_mod``. `arXiv:1601.06791 `_ .. [ZuMandelbaum2015] Zu Y. & Mandelbaum R. 2015, MNRAS 454, 1161. iHOD model: inverse SHMR approach to galaxy–halo connection via SDSS clustering and galaxy–galaxy lensing; reference for ``ZuMandelbaum15HODModel`` in ``hod_mod``. `arXiv:1505.02781 `_ .. [ZuMandelbaum2016] Zu Y. & Mandelbaum R. 2016, MNRAS 457, 4360. iHOD quenching model: Weibull CDF red fractions for centrals and satellites; reference for ``ZuMandelbaum16QuenchingModel`` in ``hod_mod``. `arXiv:1509.06758 `_ .. [Guo2018] Guo H. et al. 2018, ApJ 858, 30. Incompleteness-corrected SHMR (ICSMF) with broken power-law for SDSS main; reference for ``Guo18ICSMFModel`` in ``hod_mod``. `arXiv:1804.01993 `_ .. [Guo2019] Guo H. et al. 2019, ApJ 871, 147. 15-parameter ICSMF for eBOSS ELGs including quenched fraction; reference for ``Guo19ICSMFModel`` in ``hod_mod``. `arXiv:1810.05318 `_ .. [Zacharegkas2025] Zacharegkas G. et al. 2025. Kravtsov SHMR with threshold scatter; reference for ``Zacharegkas25HODModel`` in ``hod_mod``. `arXiv:2506.22367 `_ ---- Stellar-to-Halo Mass Relations and SHAM ----------------------------------------- Empirical and simulation-based constraints on how stellar mass maps to halo mass, used in SHAM models (``hod_mod/connection/sham.py``). .. [Moster2013] Moster B.P., Naab T. & White S.D.M. 2013, MNRAS 428, 3121. Empirical SMHM relation via abundance matching across redshifts; reference for ``smhm_moster13`` in ``hod_mod``. `arXiv:1205.5807 `_ .. [Behroozi2013] Behroozi P.S., Wechsler R.H. & Conroy C. 2013, ApJ 770, 57. SMHM relation from average star formation histories; reference for ``smhm_behroozi13`` in ``hod_mod``. `arXiv:1207.6105 `_ .. [Girelli2020] Girelli G. et al. 2020, A&A 634, A135. Stellar-to-halo mass relation over the past 12 Gyr; reference for ``smhm_girelli20`` in ``hod_mod``. `arXiv:2001.02230 `_ ---- Galaxy Clustering and Projected Correlation Function ------------------------------------------------------ Theoretical and observational works on the projected correlation function :math:`w_p(r_p)` and the power-law approximations used for model validation. .. [DavisPeebles1983] Davis M. & Peebles P.J.E. 1983, ApJ 267, 465. Introduced the projected correlation function :math:`w_p(r_p)` via line-of-sight integration to :math:`\pi_{\rm max}`; fundamental observable in HOD fitting. .. [Hamilton1992] Hamilton A.J.S. 1992, ApJ 385, L5. Linear redshift-space distortions; basis for RSD corrections in projected correlation functions. ---- Galaxy-Galaxy Lensing and Excess Surface Mass Density ------------------------------------------------------- From the first GGL detections through modern combined HOD+lensing analyses covering the full range of scales accessible to ``hod_mod``. .. [BartelmannSchneider2001] Bartelmann M. & Schneider P. 2001, Phys. Rep. 340, 291. Comprehensive review of weak gravitational lensing theory; reference for :math:`\Delta\Sigma(R)` and convergence formulas. `arXiv:astro-ph/9912508 `_ .. [Mandelbaum2005] Mandelbaum R. et al. 2005, MNRAS 361, 1287. First SDSS galaxy-galaxy lensing analysis measuring halo masses and satellite fractions across galaxy samples. `arXiv:astro-ph/0501048 `_ .. [Mandelbaum2006] Mandelbaum R. et al. 2006, MNRAS 372, 758. SDSS GGL: density profiles of galaxy groups and clusters from weak lensing; demonstrated NFW profile consistency at group scales. `arXiv:astro-ph/0605476 `_ .. [Leauthaud2017] Leauthaud A. et al. 2017, MNRAS 467, 3024. "Lensing is Low": BOSS CMASS lensing amplitude 20–40% below predictions from clustering; established the lensing–clustering discrepancy as a key diagnostic. `arXiv:1611.08606 `_ .. [Miyatake2022] Miyatake H. et al. 2022, Phys. Rev. D 106, 083520. Emulator-based HOD analysis of HSC-Y1 × SDSS: joint :math:`w_p + \Delta\Sigma` at 3–30 :math:`h^{-1}`Mpc; :math:`S_8 = 0.795^{+0.049}_{-0.042}`. Used for pipeline consistency validation. `arXiv:2111.02419 `_ .. [Lange2023] Lange J.U. et al. 2023, MNRAS 520, 5373. Full-scale :math:`w_p + \Delta\Sigma` (0.4–63 :math:`h^{-1}`Mpc) in BOSS × KiDS+DES; :math:`S_8 = 0.792 \pm 0.022`; includes small-scale HOD constraints. `arXiv:2301.08692 `_ .. [Heydenreich2025] Heydenreich S. et al. 2025. "Lensing Without Borders": :math:`\Delta\Sigma` and :math:`w_p` from DESI-DR1 cross-correlated with DES, KiDS, and HSC; data release for KP7 cosmological analyses. `arXiv:2506.21677 `_ .. [Lange2025] Lange J.U. et al. 2025. Cosmological constraints from full-scale clustering + lensing with DESI-DR1: :math:`S_8 = 0.794 \pm 0.023`, :math:`\Omega_m = 0.295 \pm 0.012`. `arXiv:2512.15962 `_ ---- Intrinsic Alignments --------------------- Progression from the first tidal alignment models through the non-linear alignment (NLA) model and its extensions, to modern observational constraints. .. [Catelan2001] Catelan P., Kamionkowski M. & Blandford R.D. 2001, MNRAS 320, L7. First tidal shear model for intrinsic alignments of elliptical galaxies; foundation of the linear alignment (LA) model. `arXiv:astro-ph/0012040 `_ .. [HirataSeljak2004] Hirata C.M. & Seljak U. 2004, Phys. Rev. D 70, 063526. Derived the gravitational torquing model and showed LA/NLA is the dominant systematic in weak lensing; NLA uses :math:`P_{\rm lin}(k)` — not :math:`P_{\rm nl}`. `arXiv:astro-ph/0406275 `_ .. [Brown2002] Brown M.L. et al. 2002, MNRAS 333, 501. Observational measurement of intrinsic alignments; defines :math:`C_1 \rho_{\rm crit,0} = 0.0134` used in the NLA amplitude. `arXiv:astro-ph/0208084 `_ .. [BridleKing2007] Bridle S. & King L. 2007, New J. Phys. 9, 444. NLA model applied to dark energy forecasts; showed IA can bias :math:`w` by ~50% if ignored; reference for :math:`A_{\rm IA}` parametrisation in ``hod_mod``. `arXiv:0705.0166 `_ .. [Blazek2019] Blazek J. et al. 2019, Phys. Rev. D 100, 103506. "Beyond linear galaxy alignments": perturbative framework including quadratic tidal terms; order-unity corrections at small scales; FAST-PT implementation. `arXiv:1708.09247 `_ .. [DESI_KP6] DESI Collaboration 2025. DESI KP6: intrinsic alignment of BGS-like lenses; :math:`A_{\rm IA} \sim 0.3{-}1.5` for stellar-mass-selected samples. `arXiv:2509.04552 `_ ---- Baryon Effects on the Matter Power Spectrum -------------------------------------------- Baryonic feedback suppresses the matter power spectrum at small scales. These works calibrate and model the suppression, motivating the baryon fraction and gas concentration models in ``hod_mod``. .. [vanDaalen2011] van Daalen M.P. et al. 2011, MNRAS 415, 3649. OWLS simulations: AGN feedback suppresses :math:`P(k)` by up to 30% at :math:`k \gtrsim 1~h/{\rm Mpc}`; first large systematic study. `arXiv:1104.1174 `_ .. [SchneiderTeyssier2015] Schneider A. & Teyssier R. 2015, JCAP 12, 049. Baryon correction model (BCM): analytic prescription for baryonic redistribution based on gas fraction and stellar feedback. `arXiv:1510.06034 `_ .. [Mead2015] Mead A.J. et al. 2015, MNRAS 454, 1958. HMcode: accurate halo model for non-linear :math:`P(k)` including baryonic feedback; models gas as an NFW profile with reduced concentration :math:`c_{\rm gas} = \eta\,c_{\rm DM}`. `arXiv:1505.07098 `_ .. [McCarthy2017] McCarthy I.G. et al. 2017, MNRAS 465, 2936. BAHAMAS: calibrated hydro simulations for large-scale structure cosmology; provides gas fractions and profiles at group–cluster scales. `arXiv:1612.06090 `_ .. [IllustrisTNG_chydro] Contreras S. et al. 2024. IllustrisTNG / MillenniumTNG: baryonic effects on halo concentration; broken power-law fit :math:`c_{\rm hydro}/c_{\rm DMO}` (Table 2) used in ``hod_mod`` for gas concentration ratio :math:`\eta(M)`. `arXiv:2409.01758 `_ .. [Schaller2025baryon] Schaller M. et al. 2025, MNRAS 539, 1337. FLAMINGO: Gaussian process emulator for baryon suppression of :math:`P(k)`; covers diverse feedback models to sub-percent accuracy. `arXiv:2410.17109 `_ .. [Schaller2025analytic] Schaller M. & Schaye J. 2025, MNRAS (accepted). Analytic redshift-independent sigmoid parametrisation of baryonic effects on :math:`P(k)` from FLAMINGO; motivates the ``BaryonFractionSigmoid`` model. `arXiv:2504.15633 `_ .. [FLAMINGO_fgas] FLAMINGO Collaboration 2025. FLAMINGO gas fraction measurements at group scales; :math:`f_b(M) < f_{b,\rm cosmic}` as implemented in ``hod_mod``. `arXiv:2510.25419 `_ *(verify: same ID as [Lange2025phz])* .. [FLAMINGO_hotgas] FLAMINGO Collaboration 2025. FLAMINGO hot gas profiles: :math:`c_{\rm gas} < c_{\rm DM}` at group–cluster scales; motivates the gas concentration ratio :math:`\eta(M)`. `arXiv:2509.10230 `_ .. [Siegel2025] Siegel J. et al. 2025, MNRAS (submitted). X-ray gas fractions + kSZ profiles + GGL: :math:`10 \pm 2\%` matter power suppression at :math:`k = 1~h/{\rm Mpc}`; validates baryon fraction model. `arXiv:2512.02954 `_ .. [Veenema2026] Veenema M. et al. 2026. Closure-radius model for the baryon fraction in halos. `arXiv:2603.13095 `_ .. [Pfeifer2025] Pfeifer S. et al. 2025. Machine-learning gas profiles: halo mass as primary driver beyond :math:`M_{\rm BH}`. `arXiv:2512.09021 `_ ---- Gas Profiles and Cross-Correlations -------------------------------------- Papers providing the gas profile parametrisations and the observational benchmarks for galaxy × tSZ and galaxy × soft X-ray cross-correlations. .. [Arnaud2010] Arnaud M., Pratt G.W., Piffaretti R. et al. 2010, A&A 517, A92. Universal pressure profile of galaxy clusters from the REXCESS sample (generalised NFW; Table 1: P₀=8.403, c₅₀₀=1.177, γ=0.3081, α=1.0510, β=5.4905, α_p=0.12). Implemented as :class:`~hod_mod.gas.PressureProfileA10`. `arXiv:0910.1234 `_ .. [Oppenheimer2025] Oppenheimer B.D. et al. 2025. DPMhalo: parametric electron density profiles for the diffuse gas around galaxies; 3 calibrated model variants with mass- and redshift-dependent normalisations. Implemented as :class:`~hod_mod.gas.GasDensityDPM`. `arXiv:2505.14782 `_ .. [Comparat2025] Comparat J. et al. 2025, A&A 697, A173. Galaxy × eROSITA eRASS:5 soft X-ray (0.5–2 keV) angular cross-correlation for 7 stellar-mass-selected LS DR10 samples (M*>10¹⁰–10¹¹·⁵ M☉); HOD + DPM gas model (Tables 3–4). Data in ``hod_mod/data/benchmarks/xray/``. `arXiv:2503.19796 `_ .. [Amodeo2021] Amodeo S. et al. 2021, Phys. Rev. D 103, 063514. ACT DR4 × BOSS: stacked tSZ and kSZ profiles around BOSS CMASS and LOWZ galaxies; 4.5σ measurement of the baryonic mass density in the warm-hot intergalactic medium. Model comparison target for ``validate_amodeo2021.py``. `arXiv:2009.05557 `_ .. [Pandey2025] Pandey S. et al. 2025. DES Year 3 × ACT DR6: 21σ detection of the lensing × tSZ cross-correlation C_ℓ^{γ,y}; constraints on baryonic feedback at group–cluster scales. Model comparison target for ``validate_pandey2025.py``. `arXiv:2506.07432 `_ ---- Surveys and Data ----------------- Key spectroscopic and imaging surveys providing the galaxy samples and weak-lensing source catalogues used in ``hod_mod`` analyses. .. [Blanton2003] Blanton M.R. et al. 2003, ApJ 592, 819. SDSS photometric survey and galaxy samples used in many HOD analyses. `arXiv:astro-ph/0209479 `_ .. [BOSS_CMASS] Anderson L. et al. 2014, MNRAS 441, 24. SDSS-III BOSS Data Releases 10 and 11; the CMASS sample is the reference HOD target in ``more2015_boss_cmass.py``. `arXiv:1312.4877 `_ .. [HSC_Aihara2018] Aihara H. et al. 2018, PASJ 70, S4. Hyper Suprime-Cam Subaru Strategic Program: overview of the survey. `arXiv:1704.05858 `_ .. [HSC_Mandelbaum2018] Mandelbaum R. et al. 2018, PASJ 70, S25. HSC-Y1 weak-lensing shape catalog; source of HSC ESD data in ``hod_mod``. `arXiv:1705.06745 `_ .. [KiDS_Heymans2021] Heymans C. et al. 2021, A&A 646, A140. KiDS-1000 multi-probe 3×2pt analysis: :math:`S_8 = 0.766^{+0.020}_{-0.014}`, 2–3σ below Planck; source of KiDS ESD data used in BGS analyses. `arXiv:2007.15632 `_ .. [DES_Abbott2022] Abbott T.M.C. et al. 2022, Phys. Rev. D 105, 023520. DES Year 3 cosmic shear: :math:`S_8 = 0.759^{+0.025}_{-0.023}`, 2.3σ below Planck; source of DES ESD data used in BGS analyses. `arXiv:2105.13544 `_ .. [DESI_EDR] DESI Collaboration 2023. DESI Early Data Release: survey overview, instrument, targeting. `arXiv:2306.06308 `_ .. [DESI_BGS_Hahn2023] Hahn C. et al. 2023, AJ 165, 253. DESI Bright Galaxy Survey: target selection, completeness, and validation. `arXiv:2208.08512 `_ .. [Comparat2023] Comparat J. et al. 2023, A&A 673, A122. eFEDS X-ray AGN HOD analysis: joint X-ray/optical galaxy–halo connection. `ADS `_ .. [Lange2024] Lange J.U. et al. 2024, MNRAS (accepted). Systematic effects in galaxy–galaxy lensing with DESI: fibre incompleteness, magnification, and intrinsic alignment for DES/HSC/KiDS sources. `arXiv:2404.09397 `_ .. [Lange2025phz] Lange J.U. et al. 2025, ApJ (accepted). Unified photometric redshift calibration for DES, HSC, and KiDS weak-lensing surveys using DESI spectroscopy; reduces photo-z systematic uncertainty. `arXiv:2510.25419 `_ *(verify: same ID as [FLAMINGO_fgas])* ---- Recent Cosmological Constraints (S₈ Tension) ---------------------------------------------- Joint analyses combining galaxy clustering with weak gravitational lensing to constrain :math:`S_8 = \sigma_8 (\Omega_m/0.3)^{0.5}`. All recent results find :math:`S_8 \approx 0.77{-}0.80`, consistently 1.5–2.5σ below Planck. The data for the DESI-DR1 analyses are described in `[Heydenreich2025]_` ("Lensing Without Borders"). Individual HOD-based and full-shape constraints: - `[Miyatake2022]_` — HSC-Y1 × SDSS, :math:`S_8 = 0.795^{+0.049}_{-0.042}` - `[Lange2023]_` — BOSS × KiDS+DES, :math:`S_8 = 0.792 \pm 0.022` - `[Porredon2025]_` — DESI-DR1 3×2pt, :math:`S_8 = 0.786^{+0.022}_{-0.019}` - `[Semenaite2025]_` — DESI-DR1 full-shape, :math:`S_8 = 0.771{-}0.791` - `[Lange2025]_` — DESI-DR1 HOD-based, :math:`S_8 = 0.794 \pm 0.023` .. [Porredon2025] Porredon A. et al. 2025, Open J. Astrophys. 9. DESI-DR1 3×2pt analysis (BGS+LRG × KiDS-1000/DES-Y3/HSC-Y3): :math:`S_8 = 0.786^{+0.022}_{-0.019}`, 1.5–2σ below Planck. `arXiv:2512.15960 `_ .. [Semenaite2025] Semenaite A. et al. 2025, Open J. Astrophys. DESI-DR1 full-shape clustering + lensing in configuration space (BGS+LRG × KiDS-1000/DES-Y3/HSC-Y3): :math:`S_8 = 0.771{-}0.791`, 1.9–2.9σ below Planck. `arXiv:2512.15961 `_ ---- Inference Methods ------------------ Statistical inference tools used in ``hod_mod`` for MAP estimation and posterior sampling. .. [Foreman-Mackey2013] Foreman-Mackey D. et al. 2013, PASP 125, 306. emcee: the MCMC Hammer — affine-invariant ensemble sampler; used in ``WpFitter.mcmc_fit()``. `arXiv:1202.3665 `_ .. [Phan2019] Phan D. et al. 2019. NumPyro: composable effects for flexible and accelerated probabilistic programming; used in ``hod_mod/inference.py`` for HMC/NUTS. `arXiv:1912.11554 `_ ---- Galaxy-Halo Connection with Non-Linear Power Spectrum ------------------------------------------------------- The standard halo model in ``hod_mod`` uses the **linear** matter power spectrum :math:`P_{\rm lin}(k)` for the 2-halo term (following More et al. 2015). A parallel literature bypasses this approximation by either (a) substituting a non-linear fitting formula / emulator for :math:`P(k)` directly into the halo-model integrals, or (b) emulating :math:`w_p(r_p)` and :math:`\Delta\Sigma(R)` end-to-end from N-body simulations. The papers below are organised chronologically within four sub-topics. *Non-linear P(k) fitting formulae.* .. [PeacockSmith2000] Peacock J.A. & Smith R.E. 2000, MNRAS 318, 1144. Derived the first analytic halo model for the non-linear matter power spectrum, decomposing :math:`P_{\rm nl}(k) = P^{\rm 1h}(k) + P^{\rm 2h}(k)` from NFW profiles and a Press-Schechter HMF; foundation for all subsequent non-linear halo-model treatments of galaxy statistics. `arXiv:astro-ph/0005010 `_ .. [Smith2003] Smith R.E. et al. 2003, MNRAS 341, 1311. HALOFIT: empirical fitting formula for :math:`P_{\rm nl}(k)` calibrated on N-body simulations over :math:`0.001 \le k \le 10\,h\,{\rm Mpc}^{-1}`; the first widely used non-linear :math:`P(k)` prescription in HOD pipelines. `arXiv:astro-ph/0207664 `_ .. [Takahashi2012] Takahashi R. et al. 2012, ApJ 761, 152. Revised HALOFIT recalibrated on higher-resolution N-body simulations; corrects ~10% errors in the original Smith et al. (2003) formula at :math:`k \gtrsim 1\,h\,{\rm Mpc}^{-1}`; default non-linear :math:`P(k)` in many HOD pipelines and in the CosmoCov / TreeCorr ecosystem. `arXiv:1208.2701 `_ .. [Mead2020] Mead A.J. et al. 2021, MNRAS 502, 1401. HMcode-2020: extended halo model for non-linear :math:`P(k)` with neutrino masses and baryonic feedback; sub-percent accuracy to :math:`k \le 10\,h\,{\rm Mpc}^{-1}`, :math:`z \le 2`; see also [Mead2015]_ for the original version. `arXiv:2009.01858 `_ *Foundational halo-model treatments of galaxy statistics.* .. [Seljak2000] Seljak U. 2000, MNRAS 318, 1144. First analytic galaxy + dark matter clustering model using NFW profiles and a Poisson HOD; showed that non-linear galaxy power spectra can be predicted from halo properties alone, motivating the modern HOD+halo-model approach. `arXiv:astro-ph/0001493 `_ .. [Scoccimarro2001] Scoccimarro R., Sheth R.K., Hui L. & Jain B. 2001, ApJ 546, 20. 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