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covariance_matrix.py
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import numpy as np
from scipy import stats as sp
def covariance_matrix(s,b,sigma,muprime=0,mu=1,tau=100):
# what about n when b is a simulated background?
# two gaussian terms?
"""
Build the covariance matrix from signal and background counts s and b.
db is the uncertainty on background data.
"""
assert( len(b) == len(s) == len(sigma) )
matrix_size = len(b) + len(s) + 1
V_inv = np.zeros((matrix_size,matrix_size),dtype=np.float64)
#add exception handling if s=/=b
## create inverse covariance matrix V^-1
for i in range(len(b)):
common_factor = (muprime*s[i]+b[i])/(mu*s[i]+b[i])**2
print common_factor
offset = len(b)+1
##Construct all the inverse covar matrix from second derivatives of Likelihood function
## mu mu
V_inv[0,0] += s[i]**2 * common_factor
## mu b
V_inv[i+1,0] = V_inv[0,i+1] = s[i] * common_factor
## mu s
V_inv[i+offset,0]=V_inv[0,i+offset] = -b[i] * common_factor + 1
## b b
V_inv[i+1,i+1] = common_factor
if sigma[i]**2 > 0.0:
V_inv[i+1,i+1] += 1.0/sigma[i]**2
## s s
V_inv[i+offset,i+offset]= mu**2 * common_factor
if s[i] > 0.0:
V_inv[i+offset,i+offset] += tau/s[i]
## b s mixed
V_inv[i+offset,i+1] = V_inv[i+1,i+offset] = mu * common_factor
print "before inversion"
print V_inv
if np.linalg.det(V_inv) == 0:
print "Zero determinant"
return np.zeros((matrix_size,matrix_size))
else:
return np.linalg.inv(V_inv)
def chisq(s,b,sigma,mu=1,tau=100):
i = 0
bPlusS = b[i] + s[i]
justB = b[i]
chisq = (bPlusS - justB)**2 / sigma[i]**2 # + MC err ** 2
return chisq
if __name__ == "__main__":
args = [[9.e1],[40.],[8.]]
mu = 1
muprime = 0
mat = covariance_matrix(*args,mu=1,muprime=0)
print mat
#print chisq(*args)
sigma_muhat_sq = mat[0,0]
sigma_muhat = np.sqrt(sigma_muhat_sq)
print 'sigma_muhat', sigma_muhat
# Cowan sect. 3.7
q_mu = (mu-muprime)**2/sigma_muhat_sq
if q_mu <= mu**2/sigma_muhat_sq:
# should always be here
F_arg = np.sqrt(q_mu) - (mu-muprime)/sigma_muhat
else:
F_arg = (q_mu - (mu**2 - 2*mu*muprime)/sigma_muhat_sq)/(2*mu/sigma_muhat)
p_val = sp.halfnorm.sf( F_arg )
print
print 'DATA ',args[1]
print 'ERR ',args[2]
print
print 'SIGNAL ',args[0]
print
print 'Significance',F_arg
print 'p',p_val, "BSM ruled out" if p_val < 0.95 else "BSM allowed"
print chisq(*args)

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