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Pure python statistic tools for high energy physics.

Project description

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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

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 ᾰobs what value of α are not rejected at a certain confidence level (typically 68%)?

  • H0: α ≤ α down or α ≥ αup
  • H1: αdown < α < αup

αdown and αup 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.

Project details


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