add testcase Hierarchical calibration model

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Hierarchical calibration model

Submitted by Carsten Burgard cburgard@cern.ch

This test implements a simple hierarchical calibration model consisting of a global calibration scale, a shared cell-to-cell spread, individual cell calibration constants, and independent calibration measurements.

The model factorizes as

$$\tau \sim \mathcal{N}(0.03, 0.01),$$ $$g_i \sim \mathcal{N}(G, \tau),$$ $$x_i \sim \mathcal{N}(g_i, \sigma_{\mathrm{meas}}),$$

where:

• globalScale (G) is the parameter of interest.
• cellSpread (τ) controls the variation of individual cell calibrations.
• cellScale_i (g_i) are latent calibration parameters for the individual calorimeter cells.
• x_i are the observed calibration measurements.

Although HS³ does not currently provide dedicated Bayesian prior objects, the same hierarchical structure can be represented using ordinary distributions. The hyperparameter cellSpread is constrained by an auxiliary distribution, while the individual cell calibration parameters are constrained by auxiliary distributions whose means depend on the global calibration scale. The measurement distributions then relate the observed calibration data to the latent cell calibration parameters. :contentReference[oaicite:0]{index=0} :contentReference[oaicite:1]{index=1}

This test verifies that HS³ can represent hierarchical statistical models by expressing each level of the hierarchy as a standard distribution and connecting them through shared parameters.

Field	Value
Testcase name	Hierarchical calibration model
Testcase ID	hierarchical_calibration_model
Schema version	0.2.9
Description	This test implements a simple hierarchical calibration model consisting of a global calibration scale, a shared cell-to-cell spread, individual cell calibration constants, and independent calibration measurements.

The model factorizes as

$$\tau \sim \mathcal{N}(0.03, 0.01),$$ $$g_i \sim \mathcal{N}(G, \tau),$$ $$x_i \sim \mathcal{N}(g_i, \sigma_{\mathrm{meas}}),$$

where:

• globalScale (G) is the parameter of interest.
• cellSpread (τ) controls the variation of individual cell calibrations.
• cellScale_i (g_i) are latent calibration parameters for the individual calorimeter cells.
• x_i are the observed calibration measurements.

Although HS³ does not currently provide dedicated Bayesian prior objects, the same hierarchical structure can be represented using ordinary distributions. The hyperparameter cellSpread is constrained by an auxiliary distribution, while the individual cell calibration parameters are constrained by auxiliary distributions whose means depend on the global calibration scale. The measurement distributions then relate the observed calibration data to the latent cell calibration parameters. :contentReference[oaicite:0]{index=0} :contentReference[oaicite:1]{index=1}

This test verifies that HS³ can represent hierarchical statistical models by expressing each level of the hierarchy as a standard distribution and connecting them through shared parameters. |
| Source | https://docs.google.com/presentation/d/1MsB_mgA46xE61NEKPJZXI8E7_E64bjBhxKmuU1yOnac/edit?slide=id.g3e80de5473d_0_244#slide=id.g3e80de5473d_0_244 |
| Modified from source | False |
| Notes | |
| Reference backend | stalbrec/hs3-testsuite-roofit-backend:e3a793 |

NLL scan scan_globalScale

Field	Value
Target	likelihood=model_data
Parameters	['globalScale']
Points	[[0.95], [0.96], [0.97], [0.98], [0.99], [1.0], [1.01], [1.02], [1.03], [1.04], [1.05]]