1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
|
# author : S. Mandalia
# s.p.mandalia@qmul.ac.uk
#
# date : April 04, 2018
"""
Likelihood functions for the BSM flavour ratio analysis
"""
from __future__ import absolute_import, division
from copy import deepcopy
from functools import partial
import numpy as np
import scipy
from scipy.stats import multivariate_normal, truncnorm
from utils import fr as fr_utils
from utils import gf as gf_utils
from utils.enums import Likelihood, ParamTag, PriorsCateg, StatCateg
from utils.misc import enum_parse, gen_identifier, parse_bool
def GaussianBoundedRV(loc=0., sigma=1., lower=-np.inf, upper=np.inf):
"""Normalised gaussian bounded between lower and upper values"""
low, up = (lower - loc) / sigma, (upper - loc) / sigma
g = scipy.stats.truncnorm(loc=loc, scale=sigma, a=low, b=up)
return g
def multi_gaussian(fr, fr_bf, sigma, offset=-320):
"""Multivariate gaussian likelihood."""
cov_fr = np.identity(3) * sigma
return np.log(multivariate_normal.pdf(fr, mean=fr_bf, cov=cov_fr)) + offset
def llh_argparse(parser):
parser.add_argument(
'--stat-method', default='bayesian',
type=partial(enum_parse, c=StatCateg), choices=StatCateg,
help='Statistical method to employ'
)
def lnprior(theta, paramset):
"""Priors on theta."""
if len(theta) != len(paramset):
raise AssertionError(
'Length of MCMC scan is not the same as the input '
'params\ntheta={0}\nparamset={1}'.format(theta, paramset)
)
for idx, param in enumerate(paramset):
param.value = theta[idx]
ranges = paramset.ranges
for value, range in zip(theta, ranges):
if range[0] <= value <= range[1]:
pass
else: return -np.inf
prior = 0
for param in paramset:
if param.prior is PriorsCateg.GAUSSIAN:
prior += GaussianBoundedRV(
loc=param.nominal_value, sigma=param.std
).logpdf(param.value)
elif param.prior is PriorsCateg.LIMITEDGAUSS:
prior += GaussianBoundedRV(
loc=param.nominal_value, sigma=param.std,
lower=param.ranges[0], upper=param.ranges[1]
).logpdf(param.value)
return prior
def triangle_llh(theta, args, asimov_paramset, llh_paramset):
"""Log likelihood function for a given theta."""
if len(theta) != len(llh_paramset):
raise AssertionError(
'Length of MCMC scan is not the same as the input '
'params\ntheta={0}\nparamset]{1}'.format(theta, llh_paramset)
)
for idx, param in enumerate(llh_paramset):
param.value = theta[idx]
hypo_paramset = asimov_paramset
for param in llh_paramset.from_tag(ParamTag.NUISANCE):
hypo_paramset[param.name].value = param.value
bin_centers = np.sqrt(args.binning[:-1]*args.binning[1:])
bin_width = np.abs(np.diff(args.binning))
spectral_index = -hypo_paramset['astroDeltaGamma'].value
source_flux = np.array(
[fr * np.power(bin_centers, spectral_index)
for fr in args.source_ratio]
).T
bsm_angles = llh_paramset.from_tag(
[ParamTag.SCALE, ParamTag.MMANGLES], values=True
)
m_eig_names = ['m21_2', 'm3x_2']
ma_names = ['s_12_2', 'c_13_4', 's_23_2', 'dcp']
if set(m_eig_names+ma_names).issubset(set(llh_paramset.names)):
mass_eigenvalues = [x.value for x in llh_paramset if x.name in m_eig_names]
sm_u = fr_utils.angles_to_u(
[x.value for x in llh_paramset if x.name in ma_names]
)
else:
mass_eigenvalues = fr_utils.MASS_EIGENVALUES
sm_u = fr_utils.NUFIT_U
if args.no_bsm:
fr = fr_utils.u_to_fr(source_flux, np.array(sm_u, dtype=np.complex256))
else:
mf_perbin = []
for i_sf, sf_perbin in enumerate(source_flux):
u = fr_utils.params_to_BSMu(
theta = bsm_angles,
dim = args.dimension,
energy = bin_centers[i_sf],
mass_eigenvalues = mass_eigenvalues,
sm_u = sm_u,
no_bsm = args.no_bsm,
texture = args.texture,
)
fr = fr_utils.u_to_fr(sf_perbin, u)
mf_perbin.append(fr)
measured_flux = np.array(mf_perbin).T
intergrated_measured_flux = np.sum(measured_flux * bin_width, axis=1)
averaged_measured_flux = (1./(args.binning[-1] - args.binning[0])) * \
intergrated_measured_flux
fr = averaged_measured_flux / np.sum(averaged_measured_flux)
flavour_angles = fr_utils.fr_to_angles(fr)
# print 'flavour_angles', map(float, flavour_angles)
for idx, param in enumerate(hypo_paramset.from_tag(ParamTag.BESTFIT)):
param.value = flavour_angles[idx]
if args.likelihood is Likelihood.GOLEMFIT:
llh = gf_utils.get_llh(hypo_paramset)
elif args.likelihood is Likelihood.GF_FREQ:
llh = gf_utils.get_llh_freq(hypo_paramset)
return llh
def ln_prob(theta, args, asimov_paramset, llh_paramset):
dc_asimov_paramset = deepcopy(asimov_paramset)
dc_llh_paramset = deepcopy(llh_paramset)
lp = lnprior(theta, paramset=dc_llh_paramset)
if not np.isfinite(lp):
return -np.inf
return lp + triangle_llh(
theta, args=args, asimov_paramset=dc_asimov_paramset,
llh_paramset=dc_llh_paramset
)
|
