lauztat 1.1.2

Pure python statistic tools for high energy physics.

Pure python statistics tools for high energy physics using zfit as a backend for maximum likelihood fits.

Tests for discovery, upper limits and confidence intervals are provided based on likelihood ratios in a frequentist approach (using pseudo-experiments) or using asymptotic formulae from “Asymptotic formulae for likelihood-based tests of new physics” [arxiv:1007.1727].

lauztat has been developed at EPFL, Lausanne Switzerland (laus’ or lauz is how the cool kids call Lausanne).

Installation

Install lauztat like any other Python package:

pip install lauztat                       # maybe with sudo or --user, or in virtualenv

Dependencies

• Numpy

• zfit

• matplotlib (optionnal)

Getting started

Usual HEP results can be recast in terms of hypothesis testing where you have to choose a null H₀ and an alternative H₁ hypothesis, H₀ being the one you want to disprove. To do a test you will need your data (and weights), a model, a loss function builder and a minimizer as input to a calculator (FrequentistCalculator or AsymptoticCalculator).

Discovery:

if you do a measurement to find signals S in a dataset and you find an excess, this test answers “is the data compatible with the background only ?” with:

• H₀: background only (S = 0)

• H₁: presence of a signal (S ≠ 0)

The test return a p-value or a significance Z. If Z ≥ 3 there is an evidence and if Z ≥ 5 a discovery of a signal.

Examples of significance computations for a gaussian peak over an exponential background are provided for the asymptotic calculator and the frequentist calculator and can be ran in mybinder.

Upper limit:

if you find a small signal excess in a dataset, but not enough to claim an evidence or a discovery, you can exclude large signal yields S:

• H₀: background + some signal (S = S₀)

• H₁: S < S₀

S₀ is adjusted to a predefined p-value, typically 5%. S₀ is the upper limit on the signal yield S with 95 % confidence level (CL = 1 - p ; p = 5 % ⟺ CL = 95%).

Examples of CLs upper limits on the signal yield for a gaussian peak over an exponential background are provided for the asymptotic calculator and the frequentist calculator and can be ran in mybinder.

Confidence interval:

if you do a measurement of a parameter α with an estimator ᾰ, given an observation ᾰ_obs what value of α are not rejected at a certain confidence level (typically 68%)?

• H₀: α ≤ α _down or α ≥ α_up

• H₁: α_down < α < α_up

α_down and α_up are adjusted such the test returns a p-value of 32%.

Examples of confidence intervals on the mean of a gaussian peak are provided for the asymptotic calculator and the frequentist calculator (Feldman and Cousins confidence interval [arxiv:9711021]) and can be ran in mybinder.