Skip to main content

statistics tools and utilities

Project description

Scikit-HEP project hepstats package: statistics tools and utilities

Scikit-HEP

PyPI PyPI - Python Version DOI Build Status Azure DevOps coverage Azure DevOps tests Binder

Installation

Install hepstats like any other Python package:

pip install hepstats

or similar (use e.g. virtualenv if you wish).

Getting Started

The hepstats module includes modeling and hypothesis tests submodules. This a quick user guide to each submodule. The binder examples are also a good way to get started.

modeling

The modeling submodule includes the Bayesian Block algorithm that can be used to improve the binning of histograms. The visual improvement can be dramatic, and more importantly, this algorithm produces histograms that accurately represent the underlying distribution while being robust to statistical fluctuations. Here is a small example of the algorithm applied on Laplacian sampled data, compared to a histogram of this sample with a fine binning.

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from hepstats.modeling import bayesian_blocks

>>> data = np.random.laplace(size=10000)
>>> blocks = bayesian_blocks(data)

>>> plt.hist(data, bins=1000, label='Fine Binning', density=True, alpha=0.6)
>>> plt.hist(data, bins=blocks, label='Bayesian Blocks', histtype='step', density=True, linewidth=2)
>>> plt.legend(loc=2)

bayesian blocks example

hypotests

This submodule provides tools to do hypothesis tests such as discovery test and computations of upper limits or confidence intervals. hepstats needs a fitting backend to perform computations such as zfit. Any fitting library can be used if their API is compatible with hepstats (see api checks).

We give here a simple example of an upper limit calculation of the yield of a Gaussian signal with known mean and sigma over an exponential background. The fitting backend used is the zfit package.

>>> import zfit
>>> from zfit.loss import ExtendedUnbinnedNLL
>>> from zfit.minimize import Minuit

>>> bounds = (0.1, 3.0)
>>> obs = zfit.Space('x', limits=bounds)

>>> bkg = np.random.exponential(0.5, 300)
>>> peak = np.random.normal(1.2, 0.1, 10)
>>> data = np.concatenate((bkg, peak))
>>> data = data[(data > bounds[0]) & (data < bounds[1])]
>>> N = data.size
>>> data = zfit.Data.from_numpy(obs=obs, array=data)

>>> lambda_ = zfit.Parameter("lambda", -2.0, -4.0, -1.0)
>>> Nsig = zfit.Parameter("Nsig", 1., -20., N)
>>> Nbkg = zfit.Parameter("Nbkg", N, 0., N*1.1)
>>> signal = Nsig * zfit.pdf.Gauss(obs=obs, mu=1.2, sigma=0.1)
>>> background = Nbkg * zfit.pdf.Exponential(obs=obs, lambda_=lambda_)
>>> loss = ExtendedUnbinnedNLL(model=signal + background, data=data)

>>> from hepstats.hypotests.calculators import AsymptoticCalculator
>>> from hepstats.hypotests import UpperLimit
>>> from hepstats.hypotests.parameters import POI, POIarray

>>> calculator = AsymptoticCalculator(loss, Minuit())
>>> poinull = POIarray(Nsig, np.linspace(0.0, 25, 20))
>>> poialt = POI(Nsig, 0)
>>> ul = UpperLimit(calculator, poinull, poialt)
>>> ul.upperlimit(alpha=0.05, CLs=True)

Observed upper limit: Nsig = 15.725784747406346
Expected upper limit: Nsig = 11.927442041887158
Expected upper limit +1 sigma: Nsig = 16.596396280677116
Expected upper limit -1 sigma: Nsig = 8.592750403611896
Expected upper limit +2 sigma: Nsig = 22.24864429383046
Expected upper limit -2 sigma: Nsig = 6.400549971360598

upper limit example

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Files for hepstats, version 0.2.1
Filename, size File type Python version Upload date Hashes
Filename, size hepstats-0.2.1-py2.py3-none-any.whl (34.9 kB) File type Wheel Python version py2.py3 Upload date Hashes View hashes
Filename, size hepstats-0.2.1.tar.gz (27.6 kB) File type Source Python version None Upload date Hashes View hashes

Supported by

Elastic Elastic Search Pingdom Pingdom Monitoring Google Google BigQuery Sentry Sentry Error logging AWS AWS Cloud computing DataDog DataDog Monitoring Fastly Fastly CDN DigiCert DigiCert EV certificate StatusPage StatusPage Status page