The bias of rebinning to a minimum of bmin=1 background counts with ftgrouppha, then using wstat to estimate background contribution

wstatrebin.py

import matplotlib.pyplot as plt
import numpy as np

def rebin(
	Nbins = 40,
	minimum = 0.1,
):
	bins = np.linspace(0, 1, Nbins)
	lam = minimum + 0 * bins
	c = np.random.poisson(lam)
	edges = np.unique([0] + (np.where(c!=0)[0]+1).tolist()[:-1] + [Nbins])
	estimate = np.zeros(Nbins) * np.nan
	for lo, hi in zip(edges[:-1], edges[1:]):
		estimate[lo:hi] = c[lo:hi].sum() / (hi - lo)
	return (estimate - lam) / lam

def simulate_many(Nsim,
	Nbins = 40,
	minimum = 0.1,
):
	return np.mean([rebin(Nbins=Nbins, minimum=minimum) for i in range(Nsim)], axis=0)

for minimum in np.linspace(0.1, 4.1, 11):
	plt.plot(100 * simulate_many(10000, Nbins=40, minimum=minimum), label='%.2f' % minimum)
plt.ylabel('Estimation error (%)')
plt.ylim(-25, 25)
plt.legend(title='counts per channel')
plt.xlabel('Channel')
plt.tight_layout()
plt.savefig('wstatrebin-counts.pdf')
plt.savefig('wstatrebin-counts.png')
plt.close()