gv_significance

Implements the formulae of Vianello 2018 for computing the significance in counting experiments.

Installation

> git clone https://github.com/giacomov/gv_significance.git
> cd gv_significance

Then you can use pip:

> pip install .

or directly the setup.py file:

> python setup.py install

Examples

See Vianello (2018) for details about these methods.

NOTE: all functions accept either single values or arrays as inputs, even though the following examples deal with single values only.

Ideal case

Compute the significance of a measurement of 100 counts with an expected background of 90 in the ideal case of no uncertainty on the background:

from gv_significance import ideal_case

ideal_case.significance(n=100, b=90)

Compute the the counts that a source must generate in order to be detected at 5 sigma with an efficiency of 90% given a background of 100 counts:

from gv_significance import ideal_case

# Note: detection_efficiency must be either 0.5, 0.9 or 0.99
ideal_case.five_sigma_threshold(B=100, detection_efficiency=0.9)

Poisson observation, Poisson background with or without systematics

Compute the significance of a measurement of 100 counts when a side measurement returned a background of 900 counts with an exposure 10x the one of the observation on-source (alpha=0.1):

from gv_significance import poisson_poisson

poisson_poisson.significance(n=100, b=900, alpha=0.1)

Alternative, one can use the $Z_Bi$ estimator described in Cousins 2008 (but be careful about the range of usability, see Vianello 2018) by doing:

from gv_significance import poisson_poisson

poisson_poisson.z_bi_significance(n=100, b=900, alpha=0.1)

If there is an additional systematic uncertainty on the background measurement of at most 10%, then:

from gv_significance import poisson_poisson

poisson_poisson.significance(n=100, b=900, alpha=0.1, k=0.1)

If there is an additional systematic uncertainty on the background measurement that is Gaussian-distributed with a sigma of 10%, then:

from gv_significance import poisson_poisson

poisson_poisson.significance(n=100, b=900, alpha=0.1, sigma=0.1)

Poisson observation, Gaussian background

Compute the significance for an observation of 100 counts when we have a background estimation procedure that gives us an expected background of 90 +/- 2.4:

from gv_significance import poisson_gaussian

poisson_gaussian.significance(n=100, b=90, sigma=2.4)