Usage¶

Event rates

Rate definition¶

For the shape analysis each experiment must define the background rate B and expected signal rate S. This is done with sn_stat.rate() function:

from sn_stat import rate
B = rate(1) #constant rate 1 event/s

#constant rate within given time range, 0 outside
S1 = rate(2,range=[0,10])

times = [0, 1., 10.]
rates = [0, 10.,0.]
S2 = rate((times,rates)) #triangular signal shape
S3 = rate((times,rates), range=[0,5]) #triangular signal shape with reduced range

Detector configuration¶

The st_stat.DetConfig defines the configuration of the detector: background conditions, analysis time window, expected signal shape.

import sn_stat as st
det1 = st.DetConfig(B=B, S=S1, time_window=[0,10])
det2 = st.DetConfig(B=st.rate(10.), S=S2, time_window=[0,5])

Significance calculation¶

There are currently two methods of significance calculation implemented: sn_stat.CountAnalysis and sn_stat.ShapeAnalysis. They can be instantiated for the given detector configuration:

By default it can be used as

ana1 = st.CountAnalysis(det1)
ana2 = st.ShapeAnalysis(det2)

They can perform two tasks:

Process measured data¶

To obtain test statistic value sn_stat.Analysis.l_val() or supernova significance sn_stat.Analysis.__call__():

ts = ... #get events from the data
t0s = np.arange(-10,10,0.01) #the assumed supernova positions we're interested in
zs = ana1(ts,t0s)
ls = ana1.l_val(ts,t0s)

Calculate expected distributions¶

We can calculate the expected distribution of the test statistics under given hypothesis using sn_stat.ShapeAnalysis.l_distr(), distribution of significance values using sn_stat.ShapeAnalysis.z_distr(), and values, corresponding to certain probability quantiles sn_stat.ShapeAnalysis.z_quant().