def __init__(self, name, phafile, bkgfile, rspfile, arffile=None):
self.name = name
# Check that all file exists
notExistant = []
inputFiles = [phafile, bkgfile, rspfile]
for i in range(3):
# The file could contain a {#} specification, like spectrum.pha{3},
# which indicate the 3rd spectrum in the spectrum.pha file
inputFiles[i] = file_utils.sanitize_filename(inputFiles[i].split("{")[0])
if not file_utils.file_existing_and_readable(inputFiles[i]):
raise IOError("File %s does not exist or is not readable" % (inputFiles[i]))
phafile, bkgfile, rspfile = inputFiles
# Check the arf, if provided
if arffile is not None:
arffile = file_utils.sanitize_filename(arffile.split("{")[0])
if not file_utils.file_existing_and_readable(arffile):
raise IOError("File %s does not exist or is not readable" % (arffile))
self.phafile = OGIPPHA(phafile, filetype="observed")
self.exposure = self.phafile.getExposure()
self.bkgfile = OGIPPHA(bkgfile, filetype="background")
self.response = Response(rspfile, arffile)
# Start with an empty mask (the user will overwrite it using the
# setActiveMeasurement method)
self.mask = numpy.asarray(numpy.ones(self.phafile.getRates().shape), numpy.bool)
# Get the counts for this spectrum
self.counts = self.phafile.getRates()[self.mask] * self.exposure
# Check that counts is positive
idx = self.counts < 0
if numpy.sum(idx) > 0:
warnings.warn(
"The observed spectrum for %s " % self.name + "has negative channels! Fixing those to zero.",
RuntimeWarning,
)
self.counts[idx] = 0
pass
# Get the background counts for this spectrum
self.bkgCounts = self.bkgfile.getRates()[self.mask] * self.exposure
# Check that bkgCounts is positive
idx = self.bkgCounts < 0
if numpy.sum(idx) > 0:
warnings.warn(
"The background spectrum for %s " % self.name + "has negative channels! Fixing those to zero.",
RuntimeWarning,
)
self.bkgCounts[idx] = 0
# Check that the observed counts are positive
idx = self.counts < 0
if numpy.sum(idx) > 0:
raise RuntimeError("Negative counts in observed spectrum %s. Data are corrupted." % (phafile))
# Keep a copy which will never be modified
self.counts_backup = numpy.array(self.counts, copy=True)
self.bkgCounts_backup = numpy.array(self.bkgCounts, copy=True)
# Effective area correction is disabled by default, i.e.,
# the nuisance parameter is fixed to 1
self.nuisanceParameters = {}
self.nuisanceParameters["InterCalib"] = Parameter("InterCalib", 1, min_value=0.9, max_value=1.1, delta=0.01)
self.nuisanceParameters["InterCalib"].fix = True
def __init__(self,name,phafile,bkgfile,rspfile):
'''
If the input files are PHA2 files, remember to specify the spectrum number, for example:
FermiGBMLike("GBM","spectrum.pha{2}","bkgfile.bkg{2}","rspfile.rsp{2}")
to load the second spectrum, second background spectrum and second response.
'''
self.name = name
#Check that all file exists
notExistant = []
if(not os.path.exists(phafile.split("{")[0])):
notExistant.append(phafile.split("{")[0])
if(not os.path.exists(bkgfile.split("{")[0])):
notExistant.append(bkgfile.split("{")[0])
if(not os.path.exists(rspfile.split("{")[0])):
notExistant.append(rspfile.split("{")[0])
if(len(notExistant)>0):
for nt in notExistant:
print("File %s does not exists!" %(nt))
raise IOError("One or more input file do not exist!")
self.phafile = OGIPPHA(phafile,filetype='observed')
self.exposure = self.phafile.getExposure()
self.bkgfile = OGIPPHA(bkgfile,filetype="background")
self.response = Response(rspfile)
#Start with an empty mask (the user will overwrite it using the
#setActiveMeasurement method)
self.mask = numpy.asarray(
numpy.ones(self.phafile.getRates().shape),
numpy.bool)
#Get the counts for this spectrum
self.counts = ( self.phafile.getRates()[self.mask]
* self.exposure )
#Check that counts is positive
idx = (self.counts < 0)
if(numpy.sum(idx) > 0):
warnings.warn("The observed spectrum for %s " % self.name +
"has negative channels! Fixing those to zero.",
RuntimeWarning)
self.counts[idx] = 0
pass
#Get the background counts for this spectrum
self.bkgCounts = ( self.bkgfile.getRates()[self.mask]
* self.exposure )
#Check that bkgCounts is positive
idx = (self.bkgCounts < 0)
if(numpy.sum(idx) > 0):
warnings.warn("The background spectrum for %s " % self.name +
"has negative channels! Fixing those to zero.",
RuntimeWarning)
self.bkgCounts[idx] = 0
#Check that the observed counts are positive
idx = self.counts < 0
if numpy.sum( idx ) > 0:
raise RuntimeError("Negative counts in observed spectrum %s. Data are corrupted." % ( phafile ))
#Keep a copy which will never be modified
self.counts_backup = numpy.array(self.counts,copy=True)
self.bkgCounts_backup = numpy.array(self.bkgCounts,copy=True)
#Effective area correction is disabled by default, i.e.,
#the nuisance parameter is fixed to 1
self.nuisanceParameters = {}
self.nuisanceParameters['InterCalib'] = Parameter("InterCalib",1,0.9,1.1,0.01,fixed=True,nuisance=True)
class GenericOGIPLike(PluginPrototype):
def __init__(self, name, phafile, bkgfile, rspfile, arffile=None):
self.name = name
# Check that all file exists
notExistant = []
inputFiles = [phafile, bkgfile, rspfile]
for i in range(3):
# The file could contain a {#} specification, like spectrum.pha{3},
# which indicate the 3rd spectrum in the spectrum.pha file
inputFiles[i] = file_utils.sanitize_filename(inputFiles[i].split("{")[0])
if not file_utils.file_existing_and_readable(inputFiles[i]):
raise IOError("File %s does not exist or is not readable" % (inputFiles[i]))
phafile, bkgfile, rspfile = inputFiles
# Check the arf, if provided
if arffile is not None:
arffile = file_utils.sanitize_filename(arffile.split("{")[0])
if not file_utils.file_existing_and_readable(arffile):
raise IOError("File %s does not exist or is not readable" % (arffile))
self.phafile = OGIPPHA(phafile, filetype="observed")
self.exposure = self.phafile.getExposure()
self.bkgfile = OGIPPHA(bkgfile, filetype="background")
self.response = Response(rspfile, arffile)
# Start with an empty mask (the user will overwrite it using the
# setActiveMeasurement method)
self.mask = numpy.asarray(numpy.ones(self.phafile.getRates().shape), numpy.bool)
# Get the counts for this spectrum
self.counts = self.phafile.getRates()[self.mask] * self.exposure
# Check that counts is positive
idx = self.counts < 0
if numpy.sum(idx) > 0:
warnings.warn(
"The observed spectrum for %s " % self.name + "has negative channels! Fixing those to zero.",
RuntimeWarning,
)
self.counts[idx] = 0
pass
# Get the background counts for this spectrum
self.bkgCounts = self.bkgfile.getRates()[self.mask] * self.exposure
# Check that bkgCounts is positive
idx = self.bkgCounts < 0
if numpy.sum(idx) > 0:
warnings.warn(
"The background spectrum for %s " % self.name + "has negative channels! Fixing those to zero.",
RuntimeWarning,
)
self.bkgCounts[idx] = 0
# Check that the observed counts are positive
idx = self.counts < 0
if numpy.sum(idx) > 0:
raise RuntimeError("Negative counts in observed spectrum %s. Data are corrupted." % (phafile))
# Keep a copy which will never be modified
self.counts_backup = numpy.array(self.counts, copy=True)
self.bkgCounts_backup = numpy.array(self.bkgCounts, copy=True)
# Effective area correction is disabled by default, i.e.,
# the nuisance parameter is fixed to 1
self.nuisanceParameters = {}
self.nuisanceParameters["InterCalib"] = Parameter("InterCalib", 1, min_value=0.9, max_value=1.1, delta=0.01)
self.nuisanceParameters["InterCalib"].fix = True
pass
def useIntercalibrationConst(self, factorLowBound=0.9, factorHiBound=1.1):
self.nuisanceParameters["InterCalib"].free()
self.nuisanceParameters["InterCalib"].set_bounds(factorLowBound, factorHiBound)
# Check that the parameter is within the provided bounds
value = self.nuisanceParameters["InterCalib"].value
if value < factorLowBound:
warnings.warn(
"The intercalibration constant was %s, lower than the provided lower bound." % (value, factorLowBound)
+ " Setting it equal to the lower bound"
)
self.nuisanceParameters["InterCalib"].setValue(float(factorLowBound))
if value > factorHiBound:
warnings.warn(
"The intercalibration constant was %s, larger than the provided hi bound." % (value, factorHiBound)
+ " Setting it equal to the hi bound"
)
self.nuisanceParameters["InterCalib"].setValue(float(factorHiBound))
def fixIntercalibrationConst(self, value=None):
if value is not None:
# Fixing the constant to the provided value
self.nuisanceParameters["InterCalib"].setValue(float(value))
else:
# Do nothing, i.e., leave the constant to the value
# it currently has
pass
self.nuisanceParameters["InterCalib"].fix()
def setActiveMeasurements(self, *args):
"""Set the measurements to be used during the analysis.
Use as many ranges as you need,
specified as 'emin-emax'. Energies are in keV. Example:
setActiveMeasurements('10-12.5','56.0-100.0')
which will set the energy range 10-12.5 keV and 56-100 keV to be
used in the analysis"""
# To implelemnt this we will use an array of boolean index,
# which will filter
# out the non-used channels during the logLike
# Now build the mask: values for which the mask is 0 will be masked
mask = numpy.zeros(self.phafile.getRates().shape)
for arg in args:
ee = map(float, arg.replace(" ", "").split("-"))
emin, emax = sorted(ee)
idx1 = self.response.energyToChannel(emin)
idx2 = self.response.energyToChannel(emax)
mask[idx1 : idx2 + 1] = True
pass
self.mask = numpy.array(mask, numpy.bool)
self.counts = self.counts_backup[self.mask]
self.bkgCounts = self.bkgCounts_backup[self.mask]
print("Now using %s channels out of %s" % (numpy.sum(self.mask), self.phafile.getRates().shape[0]))
pass
def get_name(self):
"""
Return a name for this dataset (likely set during the constructor)
"""
return self.name
pass
def set_model(self, likelihoodModel):
"""
Set the model to be used in the joint minimization.
"""
self.likelihoodModel = likelihoodModel
nPointSources = self.likelihoodModel.get_number_of_point_sources()
# This is a wrapper which iterates over all the point sources and get
# the fluxes
# We assume there are no extended sources, since the GBM cannot handle them
def diffFlux(energies):
fluxes = self.likelihoodModel.get_point_source_fluxes(0, energies)
# If we have only one point source, this will never be executed
for i in range(1, nPointSources):
fluxes += self.likelihoodModel.get_point_source_fluxes(i, energies)
return fluxes
self.diffFlux = diffFlux
# The following integrates the diffFlux function using Simpson's rule
# This assume that the intervals e1,e2 are all small, which is guaranteed
# for any reasonable response matrix, given that e1 and e2 are Monte-Carlo
# energies. It also assumes that the function is smooth in the interval
# e1 - e2 and twice-differentiable, again reasonable on small intervals for
# decent models. It might fail for models with too sharp features, smaller
# than the size of the monte carlo interval.
def integral(e1, e2):
# Simpson's rule
return (e2 - e1) / 6.0 * (self.diffFlux(e1) + 4 * self.diffFlux((e1 + e2) / 2.0) + self.diffFlux(e2))
self.response.setFunction(diffFlux, integral)
pass
def inner_fit(self):
# Effective area correction
if self.nuisanceParameters["InterCalib"].free:
# A true fit would be an overkill, and slow
# Just sample a 100 values and choose the minimum
values = numpy.linspace(
self.nuisanceParameters["InterCalib"].minValue, self.nuisanceParameters["InterCalib"].maxValue, 100
)
# I do not use getLogLike so I can compute only once the folded model
# (which is not going to change during the inner fit)
folded = self.getFoldedModel()
modelCounts = folded * self.exposure
def fitfun(cons):
self.nuisanceParameters["InterCalib"].setValue(cons)
return (-1) * self._computeLogLike(
self.nuisanceParameters["InterCalib"].value * modelCounts + self.bkgCounts
)
logLval = map(fitfun, values)
idx = numpy.argmax(logLval)
self.nuisanceParameters["InterCalib"].setValue(values[idx])
# return logLval[idx]
# Now refine with minuit
parameters = collections.OrderedDict()
parameters[(self.name, "InterCalib")] = self.nuisanceParameters["InterCalib"]
minimizer = minimization.MinuitMinimizer(fitfun, parameters)
bestFit, mlogLmin = minimizer.minimize()
return mlogLmin * (-1)
else:
return self.get_log_like()
def getFoldedModel(self):
# Get the folded model for this spectrum
# (this is the rate predicted, in cts/s)
return self.response.convolve()[self.mask]
def getModelAndData(self):
e1, e2 = (self.response.ebounds[:, 0], self.response.ebounds[:, 1])
return (
self.response.convolve()[self.mask] * self.exposure + self.bkgCounts,
e1[self.mask],
e2[self.mask],
self.counts,
)
def display(self):
# Plot the counts spectrum with residuals
model, e1, e2, counts = self.getModelAndData()
# Try to automagically decide a good constant number
# of counts, based on the input
total = numpy.sum(counts)
trials = [50, 25, 15, 5]
choice = None
for t in trials:
if total / float(t) >= 10:
choice = t
break
# If no choice worked, use the minimum, which is 5 counts
# per bin
if choice is None:
choice = 5
# Bin the data by constant counts
binner = Binner.Binner(e1, e2, counts)
ne1, ne2, nc, newModel = binner.byConstantCounts(choice, model)
# Now plot the results
fig = plt.figure()
gs = gridspec.GridSpec(2, 1, height_ratios=[2, 1])
gs.update(hspace=0)
sub = plt.subplot(gs[0])
# Plot data
ec = (ne2 + ne1) / 2.0
de = (ne2 - ne1) / 2.0
y = nc / (de * 2.0) / self.exposure
dy = numpy.sqrt(nc) / (de * 2.0) / self.exposure
sub.errorbar(ec, y, xerr=de, yerr=dy, fmt=".", capsize=0)
# Plot model
xx = numpy.append(ne1, [ne2[-1]])
yy = newModel / (2.0 * de) / self.exposure
yyy = numpy.append(yy, yy[-1])
sub.step(xx, yyy, where="post")
sub.set_xscale("log")
sub.set_yscale("log", nonposy="clip")
sub.set_ylabel(r"Counts keV$^{-1}$ s$^{-1}$")
# Now plot residuals
sub1 = plt.subplot(gs[1])
res = (yy - y) / dy
sub1.axhline(0, linestyle="--")
sub1.errorbar(ec, res, yerr=1.0, xerr=de, fmt=".", capsize=0)
sub1.set_xscale("log")
# Match the x axis
sub.set_xticks([])
sub.set_xlim([(ec - de).min(), (ec + de).max()])
sub1.set_xlim([(ec - de).min(), (ec + de).max()])
sub1.set_xlabel("Energy (keV)")
return fig
def _getModelCounts(self):
# Get the folded model for this spectrum (this is the rate predicted,
# in cts/s)
folded = self.getFoldedModel()
# Model is folded+background (i.e., we assume negligible errors on the
# background)
modelCounts = self.nuisanceParameters["InterCalib"].value * folded * self.exposure + self.bkgCounts
return modelCounts
def _computeLogLike(self, modelCounts):
idx = modelCounts > 0
return numpy.sum(
-modelCounts[idx] + self.counts[idx] * numpy.log(modelCounts[idx]) - logfactorial(self.counts[idx])
)
def get_log_like(self):
"""
Return the value of the log-likelihood with the current values for the
parameters
"""
modelCounts = self._getModelCounts()
logLike = self._computeLogLike(modelCounts)
return logLike
def get_nuisance_parameters(self):
"""
Return a list of nuisance parameter names. Return an empty list if there
are no nuisance parameters
"""
return self.nuisanceParameters.keys()
pass
class FermiGBMLike(pluginPrototype):
def __init__(self,name,phafile,bkgfile,rspfile):
'''
If the input files are PHA2 files, remember to specify the spectrum number, for example:
FermiGBMLike("GBM","spectrum.pha{2}","bkgfile.bkg{2}","rspfile.rsp{2}")
to load the second spectrum, second background spectrum and second response.
'''
self.name = name
#Check that all file exists
notExistant = []
if(not os.path.exists(phafile.split("{")[0])):
notExistant.append(phafile.split("{")[0])
if(not os.path.exists(bkgfile.split("{")[0])):
notExistant.append(bkgfile.split("{")[0])
if(not os.path.exists(rspfile.split("{")[0])):
notExistant.append(rspfile.split("{")[0])
if(len(notExistant)>0):
for nt in notExistant:
print("File %s does not exists!" %(nt))
raise IOError("One or more input file do not exist!")
self.phafile = OGIPPHA(phafile,filetype='observed')
self.exposure = self.phafile.getExposure()
self.bkgfile = OGIPPHA(bkgfile,filetype="background")
self.response = Response(rspfile)
#Start with an empty mask (the user will overwrite it using the
#setActiveMeasurement method)
self.mask = numpy.asarray(
numpy.ones(self.phafile.getRates().shape),
numpy.bool)
#Get the counts for this spectrum
self.counts = ( self.phafile.getRates()[self.mask]
* self.exposure )
#Check that counts is positive
idx = (self.counts < 0)
if(numpy.sum(idx) > 0):
warnings.warn("The observed spectrum for %s " % self.name +
"has negative channels! Fixing those to zero.",
RuntimeWarning)
self.counts[idx] = 0
pass
#Get the background counts for this spectrum
self.bkgCounts = ( self.bkgfile.getRates()[self.mask]
* self.exposure )
#Check that bkgCounts is positive
idx = (self.bkgCounts < 0)
if(numpy.sum(idx) > 0):
warnings.warn("The background spectrum for %s " % self.name +
"has negative channels! Fixing those to zero.",
RuntimeWarning)
self.bkgCounts[idx] = 0
#Check that the observed counts are positive
idx = self.counts < 0
if numpy.sum( idx ) > 0:
raise RuntimeError("Negative counts in observed spectrum %s. Data are corrupted." % ( phafile ))
#Keep a copy which will never be modified
self.counts_backup = numpy.array(self.counts,copy=True)
self.bkgCounts_backup = numpy.array(self.bkgCounts,copy=True)
#Effective area correction is disabled by default, i.e.,
#the nuisance parameter is fixed to 1
self.nuisanceParameters = {}
self.nuisanceParameters['InterCalib'] = Parameter("InterCalib",1,0.9,1.1,0.01,fixed=True,nuisance=True)
pass
def useIntercalibrationConst(self,factorLowBound=0.9,factorHiBound=1.1):
self.nuisanceParameters['InterCalib'].free()
self.nuisanceParameters['InterCalib'].setBounds(factorLowBound,factorHiBound)
#Check that the parameter is within the provided bounds
value = self.nuisanceParameters['InterCalib'].value
if( value < factorLowBound ):
warnings.warn("The intercalibration constant was %s, lower than the provided lower bound." %(value,factorLowBound) +
" Setting it equal to the lower bound")
self.nuisanceParameters['InterCalib'].setValue(float(factorLowBound))
if( value > factorHiBound):
warnings.warn("The intercalibration constant was %s, larger than the provided hi bound." %(value,factorHiBound) +
" Setting it equal to the hi bound")
self.nuisanceParameters['InterCalib'].setValue(float(factorHiBound))
def fixIntercalibrationConst(self,value=None):
if(value is not None):
#Fixing the constant to the provided value
self.nuisanceParameters['InterCalib'].setValue(float(value))
else:
#Do nothing, i.e., leave the constant to the value
#it currently has
pass
self.nuisanceParameters['InterCalib'].fix()
def setActiveMeasurements(self,*args):
'''Set the measurements to be used during the analysis.
Use as many ranges as you need,
specified as 'emin-emax'. Energies are in keV. Example:
setActiveMeasurements('10-12.5','56.0-100.0')
which will set the energy range 10-12.5 keV and 56-100 keV to be
used in the analysis'''
#To implelemnt this we will use an array of boolean index,
#which will filter
#out the non-used channels during the logLike
#Now build the mask: values for which the mask is 0 will be masked
mask = numpy.zeros(self.phafile.getRates().shape)
for arg in args:
ee = map(float,arg.replace(" ","").split("-"))
emin,emax = sorted(ee)
idx1 = self.response.energyToChannel(emin)
idx2 = self.response.energyToChannel(emax)
mask[idx1:idx2+1] = True
pass
self.mask = numpy.array(mask,numpy.bool)
self.counts = self.counts_backup[self.mask]
self.bkgCounts = self.bkgCounts_backup[self.mask]
print("Now using %s channels out of %s" %( numpy.sum(self.mask),
self.phafile.getRates().shape[0]
) )
pass
def getName(self):
'''
Return a name for this dataset (likely set during the constructor)
'''
return self.name
pass
def setModel(self,likelihoodModel):
'''
Set the model to be used in the joint minimization.
'''
self.likelihoodModel = likelihoodModel
nPointSources = self.likelihoodModel.getNumberOfPointSources()
#This is a wrapper which iterates over all the point sources and get
#the fluxes
#We assume there are no extended sources, since the GBM cannot handle them
def diffFlux(energies):
fluxes = self.likelihoodModel.getPointSourceFluxes(0,energies)
#If we have only one point source, this will never be executed
for i in range(1, nPointSources):
fluxes += self.likelihoodModel.getPointSourceFluxes(i,energies)
return fluxes
self.diffFlux = diffFlux
#The following integrates the diffFlux function using Simpson's rule
#This assume that the intervals e1,e2 are all small, which is guaranteed
#for any reasonable response matrix, given that e1 and e2 are Monte-Carlo
#energies. It also assumes that the function is smooth in the interval
#e1 - e2 and twice-differentiable, again reasonable on small intervals for
#decent models. It might fail for models with too sharp features, smaller
#than the size of the monte carlo interval.
def integral(e1,e2):
#Simpson's rule
return (e2 - e1) / 6.0 * ( self.diffFlux(e1)
+ 4 * self.diffFlux( (e1+e2) / 2.0 )
+ self.diffFlux(e2) )
self.response.setFunction( diffFlux,
integral)
pass
def innerFit(self):
#Effective area correction
if(self.nuisanceParameters['InterCalib'].isFree()):
#A true fit would be an overkill, and slow
#Just sample a 100 values and choose the minimum
values = numpy.linspace(self.nuisanceParameters['InterCalib'].minValue,
self.nuisanceParameters['InterCalib'].maxValue,
100)
#I do not use getLogLike so I can compute only once the folded model
#(which is not going to change during the inner fit)
folded = self.getFoldedModel()
modelCounts = folded * self.exposure
def fitfun(cons):
self.nuisanceParameters['InterCalib'].setValue( cons )
return (-1) * self._computeLogLike(self.nuisanceParameters['InterCalib'].value * modelCounts + self.bkgCounts)
logLval = map(fitfun, values)
idx = numpy.argmax(logLval)
self.nuisanceParameters['InterCalib'].setValue(values[idx])
#return logLval[idx]
#Now refine with minuit
parameters = collections.OrderedDict()
parameters[ (self.name, 'InterCalib') ] = self.nuisanceParameters['InterCalib']
minimizer = minimization.iMinuitMinimizer(fitfun, parameters)
bestFit, mlogLmin = minimizer.minimize()
return mlogLmin * (-1)
else:
return self.getLogLike()
def getFoldedModel(self):
#Get the folded model for this spectrum
#(this is the rate predicted, in cts/s)
return self.response.convolve()[self.mask]
def getModelAndData(self):
e1,e2 = (self.response.ebounds[:,0],
self.response.ebounds[:,1])
return ( self.response.convolve()[self.mask] * self.exposure
+ self.bkgCounts,
e1[self.mask],
e2[self.mask],
self.counts )
def _getModelCounts(self):
#Get the folded model for this spectrum (this is the rate predicted,
#in cts/s)
folded = self.getFoldedModel()
#Model is folded+background (i.e., we assume negligible errors on the
#background)
modelCounts = self.nuisanceParameters['InterCalib'].value * folded * self.exposure + self.bkgCounts
return modelCounts
def _computeLogLike(self, modelCounts):
return numpy.sum(- modelCounts
+ self.counts * numpy.log(modelCounts)
- logfactorial(self.counts) )
def getLogLike(self):
'''
Return the value of the log-likelihood with the current values for the
parameters
'''
modelCounts = self._getModelCounts()
logLike = self._computeLogLike( modelCounts )
return logLike
def getNuisanceParameters(self):
'''
Return a list of nuisance parameter names. Return an empty list if there
are no nuisance parameters
'''
return self.nuisanceParameters.keys()
pass