def calc_A_unbinned(data, bg_params, sig_params):
'''Given input data and the true distribution parameters, calculate the 95% UL for the unbinned
data. The bg and signal parameters are held fixed. The best-fit A value is determined first,
then the 95% UL is determined by scanning for the correct value of A that leads to a p-value of
0.05. This procedure must be run many times and averaged to get the mean UL value and error
bands.'''
mu = sig_params[0]
sigma = sig_params[1]
alpha = bg_params[0]
beta = bg_params[1]
gamma = bg_params[2]
params = Parameters()
params.add_many(
('C' , 0.01 , True , 0 , 1 , None , None) ,
('mu' , mu , False , None , None , None , None) ,
('sigma' , sigma , False , None , None , None , None) ,
('alpha' , alpha , False , None , None , None , None) ,
('beta' , beta , False , None , None , None , None) ,
('gamma' , gamma , False , None , None , None , None)
)
bg_sig_model = Model(bg_sig_pdf, params)
# Obtain the best fit value for A
mle_fitter = NLLFitter(bg_sig_model)
mle_res = mle_fitter.fit(np.asarray(data), calculate_corr=False,
verbose=False)
return mle_res.x[0]
def generate_initial_params(data_bg_mul2, data_bg_mul8, seed=5):
# fit to the data distributions
bg_params = Parameters()
bg_params.add_many(
('alpha', -1.80808e+01, True, 1e-20, 20, None, None),
('beta', -8.21174e-02, True, -10, -1e-20, None, None),
('gamma', 8.06289e-01, True, 1e-20, 10, None, None)
)
bg_model = Model(bg_pdf, bg_params)
bg_fitter = NLLFitter(bg_model)
bg_result = bg_fitter.fit(data_bg_mul2, calculate_corr=False)
n_bg = len(data_bg_mul8)
gRandom.SetSeed(seed)
# Set up bg sampling
bg_pdf_ROOT = functools.partial(bg_pdf, doROOT=True)
tf1_bg_pdf = TF1("tf1_bg_pdf", bg_pdf_ROOT, 2800, 13000, 3)
tf1_bg_pdf.SetParameters(*bg_result.x)
mc_bg = [tf1_bg_pdf.GetRandom() for i in range(n_bg)]
be_bg = bayesian_blocks(mc_bg, p0=0.02)
be_bg[-1] += 0.1
be_bg = np.append(be_bg, [13000])
be_bg[0] = 2800
# print be_bg
# hist(data_bg_mul8, bins=be_bg, scale='binwidth')
# plt.show()
return bg_result, n_bg, be_bg
def calc_A_cnc(data, bg_params, sig_params, xlow=2800, cache_true=None, cache_fit=None):
'''Given input data and the true template, calculate the 95% UL for a single binned
data. The bg and signal templates are held fixed. The best-fit A value is determined first,
then the 95% UL is determined by scanning for the correct value of A that leads to a p-value of
0.05. This procedure must be run many times and averaged to get the mean UL value and error
bands.'''
if cache_true is None:
cache_true = {}
if cache_fit is None:
cache_fit = {}
# Set up the models and pdfs, given the true means
data = np.asarray(data)
if xlow in cache_true:
true_bg, true_sig = cache_true[xlow]
else:
true_bg, _ = integrate.quad(functools.partial(bg_pdf, a=bg_params), xlow, 13000)
true_sig, _ = integrate.quad(functools.partial(sig_pdf, a=sig_params), xlow, 13000)
cache_true[xlow] = (true_bg, true_sig)
tmp_data = data[data > xlow]
# if len(tmp_data) is 0:
# raise Exception('no data after cut={}'.format(xlow))
if len(tmp_data) in cache_fit and xlow in cache_true:
mle_a = cache_fit[len(tmp_data)]
else:
n_tot = len(data)
template_pdf = template_pdf_wrapper([true_bg], [true_sig], cnc=True)
template_params = Parameters()
template_params.add_many(
('A' , 0.1 , True , 0 , 1 , None , None) ,
('n_tot' , n_tot , False , None , None , None , None)
)
template_model = Model(template_pdf, template_params)
template_fitter = NLLFitter(template_model)
# Obtain the best fit value for A
ntmp = len(tmp_data)
if ntmp < 3:
ntmp = 3
mle_res = template_fitter.fit(np.asarray([ntmp]), calculate_corr=False, verbose=False)
mle_a = mle_res.x[0]
cache_fit[len(tmp_data)] = mle_a
return mle_a, cache_true, cache_fit
def generate_q0_via_nll_unbinned_constrained(bg, data, bg_params):
'''Perform two nll fits to data, one for bg+signal, one for bg-only.
Use these values to create the q0 statistic.'''
data = np.asarray(data)
bg = np.asarray(bg)
_bg_params = bg_params.copy()
for p in _bg_params:
_bg_params[p].vary = False
bg_model = Model(bg_pdf, _bg_params)
mc_bg_only_fitter = NLLFitter(bg_model, verbose=False)
mc_bg_only_fitter.fit(bg, calculate_corr=False)
bg_nll = bg_model.calc_nll(None, data)
_sig_params = Parameters()
_sig_params.add_many(
('C', 0.1, True, 0, 1, None, None),
('mu', 125.77, False, 120, 130, None, None),
('sigma', 2.775, False, 1, 4, None, None),
('a1', _bg_params['a1'].value, False, -1, 1, None, None),
('a2', _bg_params['a2'].value, False, -1, 1, None, None),
('a3', _bg_params['a3'].value, False, -1, 1, None, None))
bg_sig_model = Model(bg_sig_pdf, _sig_params)
mc_bg_sig_fitter = NLLFitter(bg_sig_model, verbose=False)
mc_bg_sig_result = mc_bg_sig_fitter.fit(data, calculate_corr=False)
bg_sig_nll = mc_bg_sig_result.fun
q0 = 2 * max(bg_nll - bg_sig_nll, 0)
return q0
def generate_q0_via_shape_fit(data, bin_edges, template_params, template_pdf):
'''Generate likelihood ratios based on a template fit to the data.
Shape values for bg and signal are determined from integration of
underlying pdfs used to generate toys.
Use these values to create the q0 statistic.'''
n_tot = len(data)
bc, bin_edges = np.histogram(data, bin_edges, range=(100, 180))
_template_params = template_params.copy()
_template_params.n_tot.value = n_tot
template_model = Model(template_pdf, _template_params)
template_fitter = NLLFitter(template_model, verbose=False)
mle_res = template_fitter.fit(bc, calculate_corr=False)
nll_sig = mle_res.fun
_template_params = template_params.copy()
_template_params.n_tot.value = n_tot
_template_params.A.value = 0
_template_params.A.vary = False
template_model = Model(template_pdf, _template_params)
template_fitter = NLLFitter(template_model, verbose=False)
bg_res = template_fitter.fit(bc, calculate_corr=False)
nll_bg = bg_res.fun
q0 = 2 * (nll_bg - nll_sig)
return q0
def calc_A_binned(data, bg_mu, sig_mu):
'''Given input data and the true template, calculate the 95% UL for binned data
data. The bg and signal templates are held fixed. The best-fit A value is determined first,
then the 95% UL is determined by scanning for the correct value of A that leads to a p-value of
0.05. This procedure must be run many times and averaged to get the mean UL value and error
bands.'''
# Set up the models and pdfs, given the true means
n_tot = np.sum(data)
template_pdf = template_pdf_wrapper(bg_mu, sig_mu)
template_params = Parameters()
template_params.add_many(
('A' , 0.1 , True , 0 , 1 , None , None) ,
('n_tot' , n_tot , False , None , None , None , None)
)
template_model = Model(template_pdf, template_params)
# Obtain the best fit value for A
template_fitter = NLLFitter(template_model)
mle_res = template_fitter.fit(data, calculate_corr=False, verbose=False)
return mle_res.x[0]
def generate_initial_params(hgg_bg, hgg_signal, n_sigma):
'''Input bg and signal dataframes, and a sigma value for signal injection.
Output parameters for the pdfs that describe those distributions.'''
# grab a handful of bg events, and an ~X sigma number of signal events
hgg_bg_selection = hgg_bg[(hgg_bg.Mgg > 100)
& (hgg_bg.Mgg < 180)][0:10000].Mgg
n_bg_under_sig = hgg_bg_selection[(118 < hgg_bg_selection)
& (hgg_bg_selection < 133)].size
n_sig = int(n_sigma * np.sqrt(n_bg_under_sig))
hgg_signal_selection = hgg_signal[(hgg_signal.Mgg >= 118)
& (hgg_signal.Mgg <= 133)][0:n_sig].Mgg
data_bg = hgg_bg_selection.values
data_sig = hgg_signal_selection.values
# fit to the data distributions
bg_params = Parameters()
bg_params.add_many(('a1', 0., True, -1, 1, None, None),
('a2', 0., True, -1, 1, None, None),
('a3', 0., True, -1, 1, None, None))
bg_model = Model(bg_pdf, bg_params)
bg_fitter = NLLFitter(bg_model)
bg_result = bg_fitter.fit(data_bg, calculate_corr=False)
# bg_model = ff.Model(bg_pdf, ['a1', 'a2', 'a3'])
# bg_model.set_bounds([(-1., 1.), (-1., 1.), (-1., 1.)])
# bg_fitter = ff.NLLFitter(bg_model, data_bg)
# bg_result = bg_fitter.fit([0.0, 0.0, 0.0])
# sig_model = ff.Model(sig_pdf, ['mu', 'sigma'])
# sig_model.set_bounds([(110, 130), (1, 5)])
# sig_fitter = ff.NLLFitter(sig_model, data_sig)
# sig_result = sig_fitter.fit([120.0, 2])
sig_params = Parameters()
sig_params.add_many(
('mu', 125, True, 110, 130, None, None),
('sigma', 1, True, 1, 5, None, None),
)
sig_model = Model(sig_pdf, sig_params)
sig_fitter = NLLFitter(sig_model)
sig_result = sig_fitter.fit(data_sig)
n_bg = len(data_bg)
be_bg = bayesian_blocks(data_bg, p0=0.02)
be_sig = bayesian_blocks(data_sig, p0=0.02)
return bg_result, sig_result, n_bg, n_sig, be_bg, be_sig
def generate_q0_via_nll_unbinned(data, bg_params=None, sig_params=None):
'''Perform two nll fits to data, one for bg+signal, one for bg-only.
Use these values to create the q0 statistic.'''
if not bg_params:
_bg_params = Parameters()
_bg_params.add_many(('a1', 0., True, -1, 1, None, None),
('a2', 0., True, -1, 1, None, None),
('a3', 0., True, -1, 1, None, None))
else:
_bg_params = bg_params.copy()
for p in _bg_params:
_bg_params[p].vary = False
bg_model = Model(bg_pdf, _bg_params)
if not sig_params:
_sig_params = Parameters()
_sig_params.add_many(('C', 0.1, True, 0, 1, None, None),
('mu', 125, True, 120, 130, None, None),
('sigma', 2, True, 1, 4, None, None),
('a1', 0., True, -1, 1, None, None),
('a2', 0., True, -1, 1, None, None),
('a3', 0., True, -1, 1, None, None))
else:
_sig_params = sig_params.copy()
for p in _sig_params:
_sig_params[p].vary = False
if len(_sig_params) == 5:
_sig_params.add('C', 0.1, True, 0, 1)
bg_sig_model = Model(bg_sig_pdf, _sig_params)
mc_bg_only_fitter = NLLFitter(bg_model, verbose=False)
mc_bg_only_result = mc_bg_only_fitter.fit(np.asarray(data),
calculate_corr=False)
bg_nll = mc_bg_only_result.fun
mc_bg_sig_fitter = NLLFitter(bg_sig_model, verbose=False)
mc_bg_sig_result = mc_bg_sig_fitter.fit(np.asarray(data),
calculate_corr=False)
bg_sig_nll = mc_bg_sig_result.fun
q0 = 2 * max(bg_nll - bg_sig_nll, 0)
return q0