def mcllh_eff(actual_values, expected_values):
"""Compute the log-likelihood (llh) based on eq. 3.16 - https://doi.org/10.1007/JHEP06(2019)030
accounting for finite MC statistics.
This is the most recommended likelihood in the paper.
Parameters
----------
actual_values, expected_values : numpy.ndarrays of same shape
Returns
-------
llh : numpy.ndarray of same shape as the inputs
llh corresponding to each pair of elements in `actual_values` and
`expected_values`.
Notes
-----
*
"""
assert actual_values.shape == expected_values.shape
# Convert to simple numpy arrays containing floats
actual_values = unp.nominal_values(actual_values).ravel()
sigma = unp.std_devs(expected_values).ravel()
expected_values = unp.nominal_values(expected_values).ravel()
with np.errstate(invalid='ignore'):
# Mask off any nan expected values (these are assumed to be ok)
actual_values = np.ma.masked_invalid(actual_values)
expected_values = np.ma.masked_invalid(expected_values)
# TODO: How should we handle nan / masked values in the "data"
# (actual_values) distribution? How about negative numbers?
# Make sure actual values (aka "data") are valid -- no infs, no nans,
# etc.
if np.any((actual_values < 0) | ~np.isfinite(actual_values)):
msg = (
'`actual_values` must be >= 0 and neither inf nor nan...\n' +
maperror_logmsg(actual_values))
raise ValueError(msg)
# Check that new array contains all valid entries
if np.any(expected_values < 0.0):
msg = ('`expected_values` must all be >= 0...\n' +
maperror_logmsg(expected_values))
raise ValueError(msg)
# Replace 0's with small positive numbers to avoid inf in log
np.clip(expected_values,
a_min=SMALL_POS,
a_max=np.inf,
out=expected_values)
llh_val = likelihood_functions.poisson_gamma(actual_values,
expected_values,
sigma**2,
a=1,
b=0)
return llh_val
def thorsten_llh(actual_values, expected_values):
"""Compute the log-likelihood (llh) based on eq. 20 - https://doi.org/10.1140/epjp/i2018-12042-x
accounting for finite MC statistics. It is a good analytical approximation to the
convolutional approach described later in the paper.
Parameters
----------
actual_values, expected_values : numpy.ndarrays of same shape
Returns
-------
llh : numpy.ndarray of same shape as the inputs
llh corresponding to each pair of elements in `actual_values` and
`expected_values`.
Notes
-----
*
"""
assert actual_values.shape == expected_values.shape
# Convert to simple numpy arrays containing floats
actual_values = unp.nominal_values(actual_values).ravel()
sigma = unp.std_devs(expected_values).ravel()
expected_values = unp.nominal_values(expected_values).ravel()
with np.errstate(invalid='ignore'):
# Mask off any nan expected values (these are assumed to be ok)
actual_values = np.ma.masked_invalid(actual_values)
expected_values = np.ma.masked_invalid(expected_values)
# Check that new array contains all valid entries
if np.any(actual_values < 0):
msg = ('`actual_values` must all be >= 0...\n' +
maperror_logmsg(actual_values))
raise ValueError(msg)
# TODO: How should we handle nan / masked values in the "data"
# (actual_values) distribution? How about negative numbers?
# Make sure actual values (aka "data") are valid -- no infs, no nans,
# etc.
if np.any((actual_values < 0) | ~np.isfinite(actual_values)):
msg = (
'`actual_values` must be >= 0 and neither inf nor nan...\n' +
maperror_logmsg(actual_values))
raise ValueError(msg)
# Check that new array contains all valid entries
if np.any(expected_values < 0.0):
msg = ('`expected_values` must all be >= 0...\n' +
maperror_logmsg(expected_values))
raise ValueError(msg)
llh_val = likelihood_functions.poisson_gamma(actual_values,
expected_values,
sigma**2,
a=0,
b=0)
return llh_val