def NLL(coord):
'''
Returns the Negative Log Likelihood (NLL) for a taken tau (coord) value from a PDF
evaluated with a fixed set of 10000 t,sigma data (see "from data import...") and the
arg (coord) value.
Args:
coord: A list containing the floating point tau value(s) for which the NLL is computed
Returns:
NLL: The value of the NLL computed from the (t,sigma) dataset and input tau argument
Example:>>> NLL([0.404])
6220.45362533
>>> taulist = np.linspace(0.05,1,80)
>>> NLL([taulist])
array([ 24155.94552593, 20743.52029484, 18165.04338598, ...,
8687.56466064, 8750.85271077, 8814.00166559])
'''
tau = coord[0]
#Likelihood
LL = 0.
for i in range(0, len(t)):
#Calculate the PDF for each t,sigma value and the tau value
P = fitSig(t[i], sigma[i], tau)
#Convert the evaluated PDF for each (t,sigma) measurement into natural log form
logP = np.log(P)
#Sum all the negative log P to give the LL (positive log likelihood)
LL += logP
NLL = -LL
return NLL
def NLL5000(coord):
'''
Returns the Negative Log Likelihood (NLL) for a taken tau (coord) value from a PDF
evaluated with only the first 5000 data from a fixed set of t,sigma data
(see "from data import...") and the arg (coord) value.
Args:
coordlist: A list containing the floating point tau value(s) for which the NLL is computed
and integer value for which the dataset to draw measurements from is limited to
Returns:
NLL: The value of the NLL computed from the limited (t,sigma) dataset and input tau argument
Example:>>> NLL5000([0.404]) #
3091.461273131531
'''
tau = coord[0]
#Likelihood
LL = 0.
for i in range(0, len(t[:5000])):
#Calculate the PDF for each t,sigma value and the tau value
P = fitSig(t[i], sigma[i], tau)
#Convert the evaluated PDF for each (t,sigma) measurement into natural log form
logP = np.log(P)
#Sum all the negative log P to give the LL (positive log likelihood)
LL += logP
NLL = -LL
return NLL
def NLLBG(coord):
'''
Returns the Negative Log Likelihood (NLL) for a taken coordinate (coord) value from a PDF
evaluated with a fixed set of t,sigma data (see "from data import...") and the
arg (coord) value.
Args:
coord: A 2D array/list containing the floating point tau and a(ratio of the particle to background signal)
value in the format [tau,a] or np.array([tau,a])
Returns:
NLL: The value of the NLL computed from the (t,sigma) dataset and input coord argument
Example:>>> NLLBG([0.404,1.0])
6220.45362533
'''
#Unzip the coordinate list/array into the tau and a component
tau, a = coord
#Log Likelihood
LL = 0.
for i in range(0, len(t)):
#Calculate the PDF for each t,sigma value and the tau and a value
P = a * fitSig(t[i], sigma[i], tau) + (1 - a) * fitBG(t[i], sigma[i])
logP = np.log(P)
#Sum all the negative log P to give the LL (positive log likelihood)
LL += logP
NLL = -LL
return NLL
def NLL2500(coord):
'''
Returns the Negative Log Likelihood (NLL) for a taken tau (coord) value from a PDF
evaluated with only the first 2500 data from a fixed set of t,sigma data
(see "from data import...") and the arg (coord) value.
'''
tau = coord[0]
#Likelihood
LL = 0.
for i in range(0, len(t[:2500])):
#Calculate the PDF for each t,sigma value and the tau value
P = fitSig(t[i], sigma[i], tau)
#Convert the evaluated PDF for each (t,sigma) measurement into natural log form
logP = np.log(P)
#Sum all the negative log P to give the LL (positive log likelihood)
LL += logP
NLL = -LL
return NLL