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.. _benchmark_zumandelbaum2015_multisample:

Benchmark: Zu & Mandelbaum 2015 — Multi-Sample iHOD
=====================================================

.. list-table::
   :widths: 25 75

   * - **Model class**
     - ``ZuMandelbaum15HODModel``
   * - **Paper**
     - Zu & Mandelbaum 2015, MNRAS 454, 1161 (`arXiv:1505.02781 <https://arxiv.org/abs/1505.02781>`_)
   * - **Survey**
     - SDSS DR7, 7 stellar-mass bins from :math:`\log_{10}(M_*/h^{-2}M_\odot)\in[9.4,12.0]`
   * - **Observables**
     - :math:`w_p(r_p)` (all 7 bins) + :math:`\Delta\Sigma(R)` (5 upper bins),
       :math:`\pi_\mathrm{max} = 60\ h^{-1}\,\mathrm{Mpc}`
   * - **Cosmology**
     - WMAP7: :math:`\Omega_m=0.260,\ h=0.720,\ \sigma_8=0.770,\ n_s=0.960,\ \Omega_b=0.044`
   * - **Data source**
     - WebPlotDigitizer digitization of ZM15 Figure 6 (per-bin iHOD measurements)

Overview
--------

This benchmark tests the ``ZuMandelbaum15HODModel`` against **real digitized measurements**
from Figure 6 of Zu & Mandelbaum 2015, for each of the 7 iHOD stellar-mass bins
simultaneously.  Unlike the threshold-sample benchmark
(the single-threshold Zu & Mandelbaum 2015 benchmark), which used model-anchored data, here the data
are actual digitized point estimates from the paper figure.

The model uses the *bin HOD*: for bin :math:`[M_\mathrm{lo}, M_\mathrm{hi}]`,

.. math::

   \langle N_\mathrm{cen}^\mathrm{bin}\rangle(M_h)
     = \langle N_\mathrm{cen}^{>M_\mathrm{lo}}\rangle(M_h)
     - \langle N_\mathrm{cen}^{>M_\mathrm{hi}}\rangle(M_h)

and similarly for satellites.  This is implemented via the ``log10m_star_max`` fixed
parameter in each per-bin config.

Data
----

**WPRP files** (7 bins):

.. code-block:: none

   data/zumandelbaum2015_sdss/wp_bin_9p4_9p8.csv      (15 pts, 3-col digitized)
   data/zumandelbaum2015_sdss/wp_bin_9p8_10p2.csv     (14 pts, 3-col digitized)
   data/zumandelbaum2015_sdss/wp_bin_10p2_10p6.csv    (14 pts, 2-col digitized)
   data/zumandelbaum2015_sdss/wp_bin_10p6_11p0.csv    (14 pts, 2-col digitized)
   data/zumandelbaum2015_sdss/wp_bin_11p0_11p2.csv    (13 pts, 2-col digitized)
   data/zumandelbaum2015_sdss/wp_bin_11p2_11p4.csv    (13 pts, 2-col digitized)
   data/zumandelbaum2015_sdss/wp_bin_11p4_12p0.csv    (10 pts, 3-col digitized)

**ESD files** (5 upper bins only; lowest two bins excluded as too noisy):

.. code-block:: none

   data/zumandelbaum2015_sdss/ds_bin_10p2_10p6.csv    (16 pts, 2-col, 20% err)
   data/zumandelbaum2015_sdss/ds_bin_10p6_11p0.csv    (16 pts, 2-col, 20% err)
   data/zumandelbaum2015_sdss/ds_bin_11p0_11p2.csv    (14 pts, 3-col digitized)
   data/zumandelbaum2015_sdss/ds_bin_11p2_11p4.csv    (15 pts, 3-col digitized)
   data/zumandelbaum2015_sdss/ds_bin_11p4_12p0.csv    (13 pts, 3-col digitized)

Digitization convention:

* **3-col files** (upper/lower bounds extracted): :math:`v = \sqrt{v_\mathrm{up}\cdot v_\mathrm{lo}}`,
  :math:`\sigma = (v_\mathrm{up} - v_\mathrm{lo})/2`.
* **2-col files** (value only): :math:`\sigma = 0.15\,w_p` (WPRP) or :math:`\sigma = 0.20\,\Delta\Sigma` (ESD).

Generate CSV files from the raw txt files::

    python hod_mod/scripts/data/convert_zm15_txt_to_csv.py

Model Verification
------------------

The figure below shows predicted :math:`w_p(r_p)` and :math:`\Delta\Sigma(R)` at the
**published iHOD Table 2 parameters** versus the digitized data for all bins.

.. figure:: _images/benchmarks__zumandelbaum2015_verification__zm15_verification_all_bins.png
   :width: 100%
   :alt: ZM15 iHOD model verification — all bins at published parameters

   Verification of ``ZuMandelbaum15HODModel`` at published iHOD parameters (ZM15 Table 2)
   against digitized data from Figure 6.  Top row: :math:`w_p(r_p)`;
   bottom row: :math:`\Delta\Sigma(R)` (empty for lowest two bins).
   The :math:`\chi^2` per panel is labeled.

Regenerate::

    python hod_mod/scripts/benchmarks/plot_zm15_verification.py

Per-Bin Configurations
-----------------------

.. list-table::
   :header-rows: 1
   :widths: 18 8 8 8 15 10

   * - Bin :math:`[\log M_*]`
     - :math:`z_\mathrm{eff}`
     - :math:`\log M_\mathrm{thresh}`
     - :math:`\log M_\mathrm{max}`
     - Observable
     - Config key
   * - 9.4–9.8
     - 0.04
     - 9.4
     - 9.8
     - :math:`w_p` only
     - ``zumandelbaum2015_bin_9p4_9p8``
   * - 9.8–10.2
     - 0.055
     - 9.8
     - 10.2
     - :math:`w_p` only
     - ``zumandelbaum2015_bin_9p8_10p2``
   * - 10.2–10.6
     - 0.075
     - 10.2
     - 10.6
     - :math:`w_p + \Delta\Sigma`
     - ``zumandelbaum2015_bin_10p2_10p6``
   * - 10.6–11.0
     - 0.11
     - 10.6
     - 11.0
     - :math:`w_p + \Delta\Sigma`
     - ``zumandelbaum2015_bin_10p6_11p0``
   * - 11.0–11.2
     - 0.15
     - 11.0
     - 11.2
     - :math:`w_p + \Delta\Sigma`
     - ``zumandelbaum2015_bin_11p0_11p2``
   * - 11.2–11.4
     - 0.17
     - 11.2
     - 11.4
     - :math:`w_p + \Delta\Sigma`
     - ``zumandelbaum2015_bin_11p2_11p4``
   * - 11.4–12.0
     - 0.19
     - 11.4
     - 12.0
     - :math:`w_p + \Delta\Sigma`
     - ``zumandelbaum2015_bin_11p4_12p0``

Per-Bin MAP Results
--------------------

Each bin is fit independently with 9 free parameters
(:math:`\log M_{1h},\,\log M_{*0},\,\beta,\,\delta,\,\gamma,\,\sigma_{\ln M_*},\,\eta,\,f_c,\,B_\mathrm{sat}`)
and 6 fixed satellite/scatter parameters at published iHOD values.

.. note::
   Per-bin independent fits are **not** how ZM15 derived their parameters.  The published
   SHMR values are a *global* solution fitting all bins simultaneously.  Individual bins
   are underconstrained (9 free parameters; only 5–20 degrees of freedom per bin), so the
   per-bin MAP lands far from published values.  Use the joint fit for meaningful comparison.

Run per-bin MAP fits::

    for BIN in 9p4_9p8 9p8_10p2 10p2_10p6 10p6_11p0 11p0_11p2 11p2_11p4 11p4_12p0; do
      python hod_mod/scripts/benchmarks/run_benchmark.py \
        --model zumandelbaum2015_bin_${BIN} --plot
    done

Joint All-Samples MAP Fit
--------------------------

A single global iHOD model is fit to all 7 bins simultaneously, exactly as in the
original ZM15 iHOD analysis.  The combined log-probability is:

.. math::

   \ln P(\theta) = \ln\pi(\theta) + \sum_{i=1}^{7} \ln\mathcal{L}_i(\theta\,|\,\mathrm{data}_i)

Run (Nelder-Mead optimizer, ~2–3 hours)::

    python hod_mod/scripts/benchmarks/run_zm15_joint_all.py [--mcmc]

Results are written to ``results/benchmarks/zumandelbaum2015_joint/``.

**Joint MAP results** (digitized data, Nelder-Mead, 2110 iterations):

.. list-table::
   :header-rows: 1
   :widths: 20 12 12 12

   * - Parameter
     - MAP
     - Published
     - :math:`\Delta/\sigma`
   * - :math:`\log M_{1h}`
     - 11.74
     - 12.10
     - −2.10σ
   * - :math:`\log M_{*0}`
     - 9.79
     - 10.31
     - −5.19σ
   * - :math:`\beta`
     - 0.335
     - 0.330
     - +0.02σ ✓
   * - :math:`\delta`
     - 0.469
     - 0.420
     - +1.22σ ✓
   * - :math:`\gamma`
     - 1.331
     - 1.210
     - +0.61σ ✓
   * - :math:`\sigma_{\ln M_*}`
     - 0.813
     - 0.500
     - +7.83σ
   * - :math:`\eta`
     - −0.189
     - −0.040
     - −7.46σ
   * - :math:`f_c`
     - 0.997
     - 0.860
     - +0.98σ ✓
   * - :math:`B_\mathrm{sat}`
     - 10.69
     - 8.980
     - +1.45σ ✓

**Per-bin** :math:`\chi^2`:

.. list-table::
   :header-rows: 1
   :widths: 20 12 10 15

   * - Bin :math:`[\log M_*]`
     - :math:`\chi^2`
     - ndof
     - :math:`\chi^2/\mathrm{ndof}`
   * - 9.4–9.8
     - 20.76
     - 6
     - 3.46
   * - 9.8–10.2
     - 16.58
     - 5
     - 3.32
   * - **10.2–10.6**
     - **19.54**
     - **20**
     - **0.98 ✓**
   * - **10.6–11.0**
     - **22.40**
     - **20**
     - **1.12 ✓**
   * - 11.0–11.2
     - 39.29
     - 17
     - 2.31
   * - 11.2–11.4
     - 71.12
     - 19
     - 3.74
   * - 11.4–12.0
     - 47.31
     - 14
     - 3.38
   * - **Total**
     - **237.00**
     - **101**
     - **2.35**

The two middle bins (10.2–11.0), which have the most data points and the best digitization
quality, fit well (:math:`\chi^2/\mathrm{ndof}\approx 1`).  The dominant HOD parameters
(:math:`f_c,\,\beta,\,\gamma,\,\delta,\,B_\mathrm{sat}`) are recovered within :math:`\sim 2\sigma`.
The higher deviations in :math:`\sigma_{\ln M_*}` and :math:`\eta` reflect that these control
subtle SHMR scatter features which are difficult to recover from digitized figure data.

The starting :math:`\chi^2=664.8` at published parameters vs. the MAP :math:`\chi^2=237.0`
confirms the optimizer functions correctly: the published parameters are optimised against the
original tabulated measurements, not our digitization.

MCMC
----

Run MCMC for each bin after MAP::

    for BIN in 9p4_9p8 9p8_10p2 10p2_10p6 10p6_11p0 11p0_11p2 11p2_11p4 11p4_12p0; do
      python hod_mod/scripts/benchmarks/run_benchmark.py \
        --model zumandelbaum2015_bin_${BIN} --mcmc
    done

Run MCMC for the global joint fit::

    python hod_mod/scripts/benchmarks/run_zm15_joint_all.py --mcmc

Complete Run Commands
---------------------

All commands assume ``PYTHONPATH=/path/to/hod_mod`` and the ``halomod`` conda environment::

    # 0. Generate CSV files from txt (run once)
    python hod_mod/scripts/data/convert_zm15_txt_to_csv.py

    # 1. Verify model at published params (all bins, quick ~2 min)
    python hod_mod/scripts/benchmarks/plot_zm15_verification.py

    # 2. Per-bin MAP fits (~2 min per bin after JAX compilation)
    for BIN in 9p4_9p8 9p8_10p2 10p2_10p6 10p6_11p0 11p0_11p2 11p2_11p4 11p4_12p0; do
      python hod_mod/scripts/benchmarks/run_benchmark.py \
        --model zumandelbaum2015_bin_${BIN} --plot
    done

    # 3. Global joint MAP fit (all 7 bins, shared parameters)
    python hod_mod/scripts/benchmarks/run_zm15_joint_all.py

    # 4. MCMC per bin (slow, ~hours each)
    for BIN in 9p4_9p8 9p8_10p2 10p2_10p6 10p6_11p0 11p0_11p2 11p2_11p4 11p4_12p0; do
      python hod_mod/scripts/benchmarks/run_benchmark.py \
        --model zumandelbaum2015_bin_${BIN} --mcmc
    done

    # 5. Joint MCMC (slow)
    python hod_mod/scripts/benchmarks/run_zm15_joint_all.py --mcmc

See the other benchmark pages for the full suite summary.