def create_jointmodel(cls,parmodels,common_pars=[]):
"""Create a single giant ParameterModel out of a list of
ParameterModels"""
print("In create_joint_model")
print("parmodels:", parmodels)
all_submodels = []
all_fargs = []
all_dims = []
all_renaming = []
for i,m in enumerate(parmodels):
# Collect submodels and perform parameter renaming to avoid
# collisions, except where parameters are explicitly set
# as being common.
all_renaming += [[]]
for submodel in m.model.submodels:
temp = jtd.TransDist(submodel) # Need this to figure out parameter names
renaming = ['Exp{0}_{1} -> {1}'.format(i,par) for par in temp.args if par not in common_pars]
#print(renaming, temp.args, common_pars)
all_renaming[i] += renaming
all_submodels += [jtd.TransDist(submodel,renaming_map=renaming)]
all_dims += m.model.dims
all_fargs += m.submodel_deps
print("m:",m)
print("all_dims", m.model.dims, all_dims)
new_joint = jtd.JointDist(list(zip(all_submodels,all_dims)))
return jtm.ParameterModel(new_joint,all_fargs), all_renaming
def make_mu_model(s):
# Create new parameter mapping functions with 'mu1' and 'mu2' parameters fixed.
# The 'partial' tool from functools is super useful for this.
s_model = jtm.ParameterModel([
jtd.TransDist(sps.norm, partial(pars1, mu1=s[0])),
jtd.TransDist(sps.norm, partial(pars2, mu2=s[1]))
], [['mu'], ['mu']])
return s_model
def __init__(self,name,joint_pdf,observed,DOF):
"""Basic information:
name
joint pdf
observed data
degrees of freedom (of general model, i.e. used in gof test)
"""
self.name = name
self.joint_pdf = joint_pdf
oshape = np.array(observed).shape
if len(oshape)==1:
self.observed_data = np.array(observed)[np.newaxis,np.newaxis,:]
elif len(oshape)==3 and oshape[:2]==(1,1):
self.observed_data = observed # correct shape already
else:
raise ValueError("Shape problem with observed data supplied to experiment {0}. Shape was {1}, but should be either 1D (Ncomponents) or 3D (Ntrials=1, Ndraws=1, Ncomponents)".format(name,oshape))
self.DOF = DOF
self.tests = {}
self.general_model = jtm.ParameterModel(self.joint_pdf)
def make_mu_model(self, signal):
"""Create ParameterModel object for fitting with mu_test"""
if not 'mu' in self.tests.keys():
raise ValueError(
"Options for 'mu' test have not been defined for experiment {0}!"
.format(self.name))
# Currently we cannot apply the transform func directly to the JointDist object,
# so we have to pull it apart, apply the transformation to eah submodel, and then
# put it all back together.
transformed_submodels = []
for submodel, dim in zip(self.joint_pdf.submodels,
self.joint_pdf.dims):
args = c.get_dist_args(submodel)
# Pull out the arguments that aren't getting scaled by mu, and replace them with mu.
new_args = [
a for a in args if a not in self.tests['mu'].scale_with_mu
] + ['mu']
# Pull out the arguments that ARE scaled by mu; we only need to provide these ones,
# the other signal arguments are for some other submodel.
sig_args = [a for a in args if a in self.tests['mu'].scale_with_mu]
my_signal = {
a: signal[a]
for a in sig_args
} # extract subset of signal that applies to this submodel
transform_func = partial(
mu_parameter_mapping,
scale_with_mu=self.tests['mu'].scale_with_mu,
**my_signal)
trans_submodel = jtd.TransDist(submodel,
transform_func,
func_args=new_args)
#print('in make_mu_model:', trans_submodel.args)
transformed_submodels += [(trans_submodel, dim)]
#print("new_submodels:", transformed_submodels)
new_joint = jtd.JointDist(transformed_submodels)
return jtm.ParameterModel(new_joint)
{'parameters':[{'loc':1,'scale':1},{'loc':5.5,'scale':1}]}]
return {'weights': weights, 'parameters': pars}
# Need to put the mixture model into a trival JointModel in order to use it with ParameterModel
# Will need to have a bunch of samples from the mixture distribution for asymptotic formulae to work
# This is a good test of how well this framework scales...
def pars(eta,locx):
weights=[1-eta,eta]
pars=[{'parameters':[{'loc':locx,'scale':1.5},{'loc':5,'scale':2}]},
{'parameters':[{'loc':1,'scale':1},{'loc':5.5,'scale':1}]}]
return {'weights': weights, 'parameters': pars}
# Put it in a JointModel so we can make a ParameterModel out of it
mixj = jtd.JointModel([mix,mix])
parmix = jtm.ParameterModel(mixj,[pars,pars])
# The asymptotic formula won't work for just one sample per experiment. Need a bunch of
# samples.
Nevents = 30 # Will draw from our distribution this many times per trial
# Hmm, too many events seems to actually screw it up! This might be because
# it becomes possible to locate the MLE's at higher accuracy than the
# discretisation scale used here. Probably need to implement a real
# minimizer in order to get this correct.
# But that is a bit tough to do repeatedly!
# Can we use e.g. minuit in some python extension module code?
# Define the null hypothesis
null_parameters = {'eta':0., 'locx':2} #, 'locx2': 3}
# Get some test data (will be stored internally)
#print("x.shape:",x.shape)
# Will fit a 1D gaussian and a 2D multivariate gaussian
joint = jtd.JointModel([sps.norm,(sps.multivariate_normal,2)])
# Parameter functions:
def pars1(x1):
return {'loc': x1, 'scale': 1}
def pars2(x1,x2):
#print("x1,x2:",x1,x2)
return {'mean': np.array([x1,x2]).flatten(), # Structure here has to be a bit odd. Not sure why x1, x2 have strange dimensions.
'cov': [[1,0],[0,1]]}
model = jtm.ParameterModel(joint,[pars1,pars2])
null_parameters = {'x1': 0, 'x2': 0}
Ntrials = int(1e4)
Ndraws = 1
samples = model.simulate(Ntrials,Ndraws,null_parameters)
# Check the structure of the data we get out of this
print(c.get_data_structure(samples[0]))
trial0 = samples[0]
print(trial0.shape)
# Ok now that works, but Ndraws still now last. What happens when we extract the pdf?
def make_experiment_nocov(self, signal):
# Create the transformed pdf functions
# Also requires some parameter renaming since we use the
# same underlying function repeatedly
# poisson_part_mult = [jtd.TransDist(sps.poisson,partial(poisson_f_mult,b=self.SR_b[i]),
# ['s_{0} -> s'.format(i),
# 'theta_{0} -> theta'.format(i)])
# for i in range(self.N_SR)]
poisson_part_add = [
jtd.TransDist(
sps.poisson, partial(poisson_f_add, b=self.SR_b[i]),
['s_{0} -> s'.format(i), 'theta_{0} -> theta'.format(i)])
for i in range(self.N_SR)
]
# Using lognormal constraint on multiplicative systematic parameter
# sys_dist_mult = [jtd.TransDist(sps.lognorm,
# partial(func_nuis_lognorm_mult,
# theta_std=self.SR_b_sys[i]/self.SR_b[i]),
# ['theta_{0} -> theta'.format(i)])
# for i in range(self.N_SR)]
# Using normal constaint on additive systematic parameter
sys_dist_add = [
jtd.TransDist(
sps.norm,
partial(func_nuis_norm_add, theta_std=self.SR_b_sys[i]),
['theta_{0} -> theta'.format(i)]) for i in range(self.N_SR)
]
# Median data under background-only hypothesis
expected_data = np.concatenate(
[np.round(self.SR_b), np.zeros(self.N_SR)], axis=-1)
expected_data = expected_data[
np.newaxis, np.newaxis, :] # Add required extra axes.
#print("fractional systematic uncertainties:")
#print([self.SR_b_sys[i]/self.SR_b[i] for i in range(self.N_SR)])
#quit()
# This next part is a little tricky. We DON'T know the correlations
# between signal regions here, so we follow the method used in
# ColliderBit and choose just one signal region to use in our test,
# by picking, in advance, the region with the best sensitivity to
# the signal that we are interested in.
# That is, the signal region with the highest value of
# Delta LogL = LogL(n=b|s,b) - LogL(n=b|s=0,b)
# is selected.
#
# So, we need to compute this for all signal regions.
seedf = self.seeds_null_f_gof()
seedb = seedf(
expected_data,
signal) # null hypothesis fits depend on signal parameters
zero_signal = {'s_{0}'.format(i): 0 for i in range(self.N_SR)}
seed = seedf(expected_data, zero_signal)
LLR = []
for i in range(self.N_SR):
model = jtm.ParameterModel([poisson_part_add[i]] +
[sys_dist_add[i]])
odata = np.array([np.round(self.SR_b[i])] +
[0]) # median expected background-only data
si = 's_{0}'.format(i)
ti = 'theta_{0}'.format(i)
parsb = {ti: seedb[ti], **zero_signal}
pars = {ti: seed[ti], **signal}
Lmaxb = model.logpdf(parsb, odata)
Lmax = model.logpdf(pars, odata)
LLR += [-2 * (Lmax - Lmaxb)]
# Select region with largest expected (background-only) LLR for this signal
selected = np.argmax(LLR)
print("Selected signal region {0} ({1}) in analysis {2}".format(
selected, self.SR_names[selected], self.name))
# Create the joint PDF object
#joint = jtd.JointDist(poisson_part_mult + sys_dist_mult)
joint = jtd.JointDist([poisson_part_add[selected]] +
[sys_dist_add[selected]])
theta_opt = {'theta_{0}'.format(selected): 0} # additive
theta_opt2 = {
'error_theta_{0}'.format(selected): 1. * self.SR_b_sys[selected]
} # Get good step sizes from systematic error estimate
s_opt = {
's_{0}'.format(selected): 0
} # Maybe zero is a good starting guess? Should use seeds that guess based on data.
s_opt2 = {
'error_s_{0}'.format(selected): 0.1 * self.SR_b_sys[selected]
} # Get good step sizes from systematic error estimate
s_options = {**s_opt, **s_opt2}
nuis_options = {**theta_opt, **theta_opt2} #, 'print_level':1}
general_options = {**s_options, **nuis_options}
# # Set options for parameter fitting
# #theta_opt = {'theta_{0}'.format(i) : 1 for i in range(self.N_SR)} # multiplicative
# theta_opt = {'theta_{0}'.format(i) : 0 for i in range(self.N_SR)} # additive
# theta_opt2 = {'error_theta_{0}'.format(i) : 1.*self.SR_b_sys[i] for i in range(self.N_SR)} # Get good step sizes from systematic error estimate
# s_opt = {'s_{0}'.format(i): 0 for i in range(self.N_SR)} # Maybe zero is a good starting guess? Should use seeds that guess based on data.
# s_opt2 = {'error_s_{0}'.format(i) : 0.1*self.SR_b_sys[i] for i in range(self.N_SR)} # Get good step sizes from systematic error estimate
# s_options = {**s_opt, **s_opt2}
# nuis_options = {**theta_opt, **theta_opt2} #, 'print_level':1}
# general_options = {**s_options, **nuis_options}
# print("Setup for experiment {0}".format(self.name))
# #print("general_options:", general_options)
# #print("s_MLE:", self.s_MLE)
# #print("N_SR:", self.N_SR)
# #print("observed_data:", observed_data.shape)
# oseed = self.seeds_full_f_mult()(np.array(observed_data)[np.newaxis,np.newaxis,:])
# print("parameter, MLE, data, seed")
# for i in range(self.N_SR):
# par = "s_{0}".format(i)
# print("{0}, {1}, {2}, {3}".format(par, self.s_MLE[i], observed_data[i], oseed[par]))
# for i in range(self.N_SR):
# par = "theta_{0}".format(i)
# print("{0}, {1}, {2}, {3}".format(par, 1, observed_data[i+self.N_SR], oseed[par]))
# quit()
# Define the experiment object and options for fitting during statistical tests
odata = np.array([self.SR_n[selected]] +
[0]) # median expected background-only data
e = Experiment(self.name, joint, odata, DOF=1)
e.define_gof_test(
test_pars={
**s_opt,
**theta_opt
}, # Just for testing purposes
null_options=nuis_options,
full_options=general_options,
null_seeds=(self.seeds_null_f_gof(selected), True),
full_seeds=(
self.seeds_full_f_add(selected), True
), # Extra flag indicates that the "seeds" are actually the analytically exact MLEs, so no numerical minimisation needed
diagnostics=[
self.make_dfull(s_opt, theta_opt, selected),
self.make_dnull(theta_opt, selected),
])
# self.make_seedcheck(),
# self.make_checkpdf()]
#)
e.define_mu_test(nuisance_par_null=theta_opt,
null_options=nuis_options,
null_seeds=self.seeds_null_f_gof(selected),
scale_with_mu=['s_{0}'.format(selected)],
test_signal=self.test_signal)
# Just check that pdf calculation gives expected answer:
# pars = {**s_opt,**theta_opt}
# x = np.zeros(self.N_SR)
# logpdf = e.general_model.logpdf(pars,e.observed_data)
# expected_logpdf = [sps.poisson.logpmf(self.SR_n[i],self.SR_b[i]+pars['s_{0}'.format(i)]+pars['theta_{0}'.format(i)]) for i in range(self.N_SR)] \
# + [sps.norm.logpdf(x[i],loc=pars['theta_{0}'.format(i)],scale=self.SR_b_sys[i]) for i in range(self.N_SR)]
# print('logpdf :',logpdf)
# print('expected logpdf:', np.sum(expected_logpdf))
# print("Components:")
# for l, el in zip(e.general_model.logpdf_list(pars,e.observed_data), expected_logpdf):
# print(' logpdf:{0}, exp:{1}'.format(l[0][0],el))
return e
# parmodel = jtm.ParameterModel.fromList(submodels)
# Could also construct it like this:
# jointmodel = jtd.JointModel([jtd.TransDist(sps.norm,pars2_A),
# jtd.TransDist(sps.norm,pars2_B),
# jtd.TransDist(sps.norm,pars2_C)])
# parmodel = jtm.ParameterModel(jointmodel,[['mu1'],['mu2'],['mu3']])
#
# Or like this:
#parmodel = jtm.ParameterModel([jtd.TransDist(sps.norm,pars2_A),
# jtd.TransDist(sps.norm,pars2_B),
# jtd.TransDist(sps.norm,pars2_C)]
# ,[['mu1'],['mu2'],['mu3']])
# Or like this, utilising manual parameter name remapping:
parmodel = jtm.ParameterModel([(sps.norm, pars, ['mu1 -> mu']),
(sps.norm, pars, ['mu2 -> mu']),
(sps.norm, pars, ['mu3 -> mu'])])
# Or just like this:
#parmodel = jtm.ParameterModel([(sps.norm,pars2_A),
# (sps.norm,pars2_B),
# (sps.norm,pars2_C)])
# Leaving the parameters to be inferred automagically
# Define the null hypothesis
null_parameters = {'mu1': 0, 'mu2': 0, 'mu3': 0}
# Get some test data (will be stored internally)
parmodel.simulate(10000, null_parameters)
# Set ranges for parameter "scan"
ranges = {}
theta_fs_noc = []
for i in range(N_regions):
func_def = func_template_noc.format(i=i)
if i == 0:
print("Defined function:")
print(func_def)
exec(func_def)
theta_fs_noc += [f]
# Create the joint PDF objects
joint = jtd.JointModel(poisson_part + correlations)
joint_noc = jtd.JointModel(poisson_part + no_correlations)
# Connect the joint PDFs to the parameter structures
model = jtm.ParameterModel(joint, poisson_fs + [multnorm_f])
model_noc = jtm.ParameterModel(joint_noc, poisson_fs_nomu + theta_fs_noc)
# Check the inferred block structures
print("model.blocks :", model.blocks)
print("model_noc.blocks:", model_noc.blocks)
# Define null parameters
null_s = {"s_{0}".format(i): 0 for i in range(N_regions)}
null_theta = {"theta_{0}".format(i): 0 for i in range(N_regions)}
null_parameters = {"mu": 0, **null_s, **null_theta}
# In order to perform some statistical test, we need a signal
# hypothesis. It is sort of cheating, but for testing let's just use
# the observed counts for this job. In reality we should use e.g. the
# predictions from our best fit MSSM point.
def pars2_B(mu2):
return {"loc": mu2, "scale": 1}
def pars2_C(mu3):
return {"loc": mu3, "scale": 1}
jointmodel = jtd.JointModel([
jtd.TransDist(sps.norm, pars2_A),
jtd.TransDist(sps.norm, pars2_B),
jtd.TransDist(sps.norm, pars2_C)
])
parmodel = jtm.ParameterModel(jointmodel, [['mu1'], ['mu2'], ['mu3']])
# Define the null hypothesis
null_parameters = {'mu1': 0, 'mu2': 0, 'mu3': 0, 'mu4': 0}
# Get some test data (will be stored internally)
parmodel.simulate(10000, null_parameters)
# Set ranges for parameter "scan"
ranges = {}
for p in null_parameters.keys():
ranges[p] = (-5, 5)
# N gives the number of grid points in each parameter direction
options = {"ranges": ranges, "N": 20}
s_MLE = [1.5, 1.5]
# Create parameter mappings
# Proxy for 'signal strength' parameter added
def pars1(mu, mu1):
return {"loc": b[0] + mu * mu1, "scale": 1}
def pars2(mu, mu2):
return {"loc": b[1] + mu * mu2, "scale": 1}
# Create the joint PDF object
general_model = jtm.ParameterModel(
[jtd.TransDist(sps.norm, pars1),
jtd.TransDist(sps.norm, pars2)])
# Create the "observed" data
# Need extra axes for matching shape of many simulated datasets
observed_data = np.array([6.5, 7.5])[np.newaxis, np.newaxis, :]
# Define the null hypothesis
null_parameters = {'mu': 0, 'mu1': 0, 'mu2': 0}
# Define functions to get good starting guesses for fitting simulated data
def get_seeds(samples):
X1 = samples[..., 0]
X2 = samples[..., 1]
return {'mu1': X1 - b[0], 'mu2': X2 - b[1]}
# Parameter space setup
def pars1(mu1):
return {"loc": mu1, "scale": 1}
def pars2(mu2):
return {"loc": mu2, "scale": 1}
def pars3(mu3):
return {"loc": mu3, "scale": 1}
parfs = [pars1, pars2, pars3]
parmodel = jtm.ParameterModel(test_model, parfs)
# Define the null hypothesis
null_parameters = {'mu1': 0, 'mu2': 0, 'mu3': 0}
# Step 2: Set observed data
# -------------------------
fit_data = np.array([0, 0, 0])[np.newaxis, np.newaxis, :]
obs_data = np.array([2, 2, 2])[np.newaxis, np.newaxis, :]
# Step 3: Set up PyMC scan
# ------------------------
# Priors
mu1 = mc.Uniform('mu1', lower=-20, upper=20)
mu2 = mc.Uniform('mu2', lower=-20, upper=20)
