# 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
>>> model = pyhf.simplemodels.hepdata_like(signal_data=[12.0, 11.0], bkg_data=[50.0, 52.0], bkg_uncerts=[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, qtilde=True, return_expected=True)
>>> print(f"Observed: {CLs_obs}, Expected: {CLs_exp}")
Observed: 0.05251497423736956, Expected: 0.06445320535890459
```

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

```
>>> import pyhf
>>> import requests
>>> 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, qtilde=True, return_expected=True)
>>> print(f"Observed: {CLs_obs}, Expected: {CLs_exp}")
Observed: 0.3599840922126626, Expected: 0.3599840922126626
```

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

provides which
should produce the following JSON output:

```
$ 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
{
"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

- 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

☐ Non-asymptotic calculators

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
import pyhf.contrib.viz.brazil
pyhf.set_backend("numpy")
model = pyhf.simplemodels.hepdata_like(
signal_data=[10.0], bkg_data=[50.0], bkg_uncerts=[7.0]
)
data = [55.0] + model.config.auxdata
poi_vals = np.linspace(0, 5, 41)
results = [
pyhf.infer.hypotest(test_poi, data, model, qtilde=True, return_expected_set=True)
for test_poi in poi_vals
]
fig, ax = plt.subplots()
fig.set_size_inches(7, 5)
ax.set_xlabel(r"$\mu$ (POI)")
ax.set_ylabel(r"$\mathrm{CL}_{s}$")
pyhf.contrib.viz.brazil.plot_results(ax, poi_vals, results)
```

**pyhf**

**ROOT**

## A two bin example¶

```
import pyhf
import numpy as np
import matplotlib.pyplot as plt
import pyhf.contrib.viz.brazil
pyhf.set_backend("numpy")
model = pyhf.simplemodels.hepdata_like(
signal_data=[30.0, 45.0], bkg_data=[100.0, 150.0], bkg_uncerts=[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, qtilde=True, return_expected_set=True)
for test_poi in poi_vals
]
fig, ax = plt.subplots()
fig.set_size_inches(7, 5)
ax.set_xlabel(r"$\mu$ (POI)")
ax.set_ylabel(r"$\mathrm{CL}_{s}$")
pyhf.contrib.viz.brazil.plot_results(ax, poi_vals, results)
```

**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 Stack Overflow
with the `[pyhf]`

tag, which the `pyhf`

dev team
watches.

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`

is

```
@software{pyhf,
author = "{Heinrich, Lukas and Feickert, Matthew and Stark, Giordon}",
title = "{pyhf: v0.5.4}",
version = {0.5.4},
doi = {10.5281/zenodo.1169739},
url = {https://github.com/scikit-hep/pyhf},
}
```

## Authors¶

`pyhf`

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

Please check the contribution statistics for a list of contributors.

## 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).