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Warning: This is a development version. The latest stable version is at ReadTheDocs. # pure-python fitting/limit-setting/interval estimation HistFactory-style

The HistFactory p.d.f. template [CERN-OPEN-2012-016] is per-se independent of its implementation in ROOT and sometimes, it’s useful to be able to run statistical analysis outside of ROOT, RooFit, RooStats framework.

This repo is a pure-python implementation of that statistical model for multi-bin histogram-based analysis and its interval estimation is based on the asymptotic formulas of “Asymptotic formulae for likelihood-based tests of new physics” [arXiv:1007.1727]. The aim is also to support modern computational graph libraries such as PyTorch and TensorFlow in order to make use of features such as autodifferentiation and GPU acceleration.

## Hello World

This is how you use the `pyhf` Python API to build a statistical model and run basic inference:

```>>> import pyhf
>>> pyhf.set_backend("numpy")
>>> model = pyhf.simplemodels.uncorrelated_background(
...     signal=[12.0, 11.0], bkg=[50.0, 52.0], bkg_uncertainty=[3.0, 7.0]
... )
>>> data = [51, 48] + model.config.auxdata
>>> test_mu = 1.0
>>> CLs_obs, CLs_exp = pyhf.infer.hypotest(
...     test_mu, data, model, test_stat="qtilde", return_expected=True
... )
>>> print(f"Observed: {CLs_obs:.9f}, Expected: {CLs_exp:.9f}")
Observed: 0.052514974, Expected: 0.064453205
```

Alternatively the statistical model and observational data can be read from its serialized JSON representation (see next section).

```>>> import pyhf
>>> import requests
>>> pyhf.set_backend("numpy")
>>> wspace = pyhf.Workspace(requests.get("https://git.io/JJYDE").json())
>>> model = wspace.model()
>>> data = wspace.data(model)
>>> test_mu = 1.0
>>> CLs_obs, CLs_exp = pyhf.infer.hypotest(
...     test_mu, data, model, test_stat="qtilde", return_expected=True
... )
>>> print(f"Observed: {CLs_obs:.9f}, Expected: {CLs_exp:.9f}")
Observed: 0.359984092, Expected: 0.359984092
```

Finally, you can also use the command line interface that `pyhf` provides

```\$ cat << EOF  | tee likelihood.json | pyhf cls
{
"channels": [
{ "name": "singlechannel",
"samples": [
{ "name": "signal",
"data": [12.0, 11.0],
"modifiers": [ { "name": "mu", "type": "normfactor", "data": null} ]
},
{ "name": "background",
"data": [50.0, 52.0],
"modifiers": [ {"name": "uncorr_bkguncrt", "type": "shapesys", "data": [3.0, 7.0]} ]
}
]
}
],
"observations": [
{ "name": "singlechannel", "data": [51.0, 48.0] }
],
"measurements": [
{ "name": "Measurement", "config": {"poi": "mu", "parameters": []} }
],
"version": "1.0.0"
}
EOF
```

which should produce the following JSON output:

```{
"CLs_exp": [
0.0026062609501074576,
0.01382005356161206,
0.06445320535890459,
0.23525643861460702,
0.573036205919389
],
"CLs_obs": 0.05251497423736956
}
```

## What does it support

Implemented variations:
• ☑ HistoSys

• ☑ OverallSys

• ☑ ShapeSys

• ☑ NormFactor

• ☑ Multiple Channels

• ☑ Import from XML + ROOT via uproot

• ☑ ShapeFactor

• ☑ StatError

• ☑ Lumi Uncertainty

• ☑ Non-asymptotic calculators

Computational Backends:
• ☑ NumPy

• ☑ PyTorch

• ☑ TensorFlow

• ☑ JAX

Optimizers:
• ☑ SciPy (`scipy.optimize`)

• ☑ MINUIT (`iminuit`)

All backends can be used in combination with all optimizers. Custom user backends and optimizers can be used as well.

## Todo

• ☐ StatConfig

results obtained from this package are validated against output computed from HistFactory workspaces

## A one bin example

```import pyhf
import numpy as np
import matplotlib.pyplot as plt
from pyhf.contrib.viz import brazil

pyhf.set_backend("numpy")
model = pyhf.simplemodels.uncorrelated_background(
signal=[10.0], bkg=[50.0], bkg_uncertainty=[7.0]
)
data = [55.0] + model.config.auxdata

poi_vals = np.linspace(0, 5, 41)
results = [
pyhf.infer.hypotest(
test_poi, data, model, test_stat="qtilde", return_expected_set=True
)
for test_poi in poi_vals
]

fig, ax = plt.subplots()
fig.set_size_inches(7, 5)
brazil.plot_results(poi_vals, results, ax=ax)
fig.show()
```

pyhf ROOT ## A two bin example

```import pyhf
import numpy as np
import matplotlib.pyplot as plt
from pyhf.contrib.viz import brazil

pyhf.set_backend("numpy")
model = pyhf.simplemodels.uncorrelated_background(
signal=[30.0, 45.0], bkg=[100.0, 150.0], bkg_uncertainty=[15.0, 20.0]
)
data = [100.0, 145.0] + model.config.auxdata

poi_vals = np.linspace(0, 5, 41)
results = [
pyhf.infer.hypotest(
test_poi, data, model, test_stat="qtilde", return_expected_set=True
)
for test_poi in poi_vals
]

fig, ax = plt.subplots()
fig.set_size_inches(7, 5)
brazil.plot_results(poi_vals, results, ax=ax)
fig.show()
```

pyhf ROOT ## Installation

To install `pyhf` from PyPI with the NumPy backend run

```python -m pip install pyhf
```

and to install `pyhf` with all additional backends run

```python -m pip install pyhf[backends]
```

or a subset of the options.

To uninstall run

```python -m pip uninstall pyhf
```

## Questions

If you have a question about the use of `pyhf` not covered in the documentation, please ask a question on the GitHub Discussions.

If you believe you have found a bug in `pyhf`, please report it in the GitHub Issues. If you’re interested in getting updates from the `pyhf` dev team and release announcements you can join the `pyhf-announcements` mailing list.

## Citation

As noted in Use and Citations, the preferred BibTeX entry for citation of `pyhf` includes both the Zenodo archive and the JOSS paper:

```@software{pyhf,
author = {Lukas Heinrich and Matthew Feickert and Giordon Stark},
title = "{pyhf: v0.6.3}",
version = {0.6.3},
doi = {10.5281/zenodo.1169739},
url = {https://doi.org/10.5281/zenodo.1169739},
note = {https://github.com/scikit-hep/pyhf/releases/tag/v0.6.3}
}

@article{pyhf_joss,
doi = {10.21105/joss.02823},
url = {https://doi.org/10.21105/joss.02823},
year = {2021},
publisher = {The Open Journal},
volume = {6},
number = {58},
pages = {2823},
author = {Lukas Heinrich and Matthew Feickert and Giordon Stark and Kyle Cranmer},
title = {pyhf: pure-Python implementation of HistFactory statistical models},
journal = {Journal of Open Source Software}
}
```

## Authors

`pyhf` is openly developed by Lukas Heinrich, Matthew Feickert, and Giordon Stark.

Please check the contribution statistics for a list of contributors.

## Milestones

• 2020-07-28: 1000 GitHub issues and pull requests. (See PR #1000)

## Acknowledgements

Matthew Feickert has received support to work on `pyhf` provided by NSF cooperative agreement OAC-1836650 (IRIS-HEP) and grant OAC-1450377 (DIANA/HEP).