def getStandardPriors(data, options):
"""sets the standard Priors
function priors = getStandardPriors(data,options)
The priors set here are the ones used if the user does supply own priors.
Thus this functions constitutes a way to change the priors permanently
note here that the priors here are not normalized. Psignifit takes care
of the normalization implicitly. """
priors = []
""" threshold """
xspread = options['stimulusRange'][1]-options['stimulusRange'][0]
''' we assume the threshold is in the range of the data, for larger or
smaller values we tapre down to 0 with a raised cosine across half the
dataspread '''
priors.append(lambda x: prior1(x,xspread,options['stimulusRange']))
"""width"""
# minimum = minimal difference of two stimulus levels
widthmin = options['widthmin']
widthmax = xspread
''' We use the same prior as we previously used... e.g. we use the factor by
which they differ for the cumulative normal function'''
Cfactor = (my_norminv(.95,0,1) - my_norminv(.05,0,1))/( my_norminv(1-options['widthalpha'],0,1) - my_norminv(options['widthalpha'],0,1))
priors.append(lambda x: prior2(x,Cfactor, widthmin, widthmax))
""" asymptotes
set asymptote prior to the 1, 10 beta prior, which corresponds to the
knowledge obtained from 9 correct trials at infinite stimulus level
"""
priors.append(lambda x: my_betapdf(x,1,10))
priors.append(lambda x: my_betapdf(x,1,10))
""" sigma """
be = options['betaPrior']
priors.append(lambda x: my_betapdf(x,1,be))
return priors
def __call__(self):
import sys
return getStandardPriors(sys.argv[1], sys.argv[2])
def getStandardPriors(data, options):
"""sets the standard Priors
function priors = getStandardPriors(data,options)
The priors set here are the ones used if the user does supply own priors.
Thus this functions constitutes a way to change the priors permanently
note here that the priors here are not normalized. Psignifit takes care
of the normalization implicitly. """
priors = []
""" threshold """
xspread = options['stimulusRange'][1] - options['stimulusRange'][0]
''' we assume the threshold is in the range of the data, for larger or
smaller values we tapre down to 0 with a raised cosine across half the
dataspread '''
priors.append(lambda x: prior1(x, xspread, options['stimulusRange']))
"""width"""
# minimum = minimal difference of two stimulus levels
widthmin = options['widthmin']
widthmax = xspread
''' We use the same prior as we previously used... e.g. we use the factor by
which they differ for the cumulative normal function'''
Cfactor = (my_norminv(.95, 0, 1) - my_norminv(.05, 0, 1)) / (
my_norminv(1 - options['widthalpha'], 0, 1) -
my_norminv(options['widthalpha'], 0, 1))
priors.append(lambda x: prior2(x, Cfactor, widthmin, widthmax))
""" asymptotes
set asymptote prior to the 1, 10 beta prior, which corresponds to the
knowledge obtained from 9 correct trials at infinite stimulus level
"""
priors.append(lambda x: my_betapdf(x, 1, 10))
priors.append(lambda x: my_betapdf(x, 1, 10))
""" sigma """
be = options['betaPrior']
priors.append(lambda x: my_betapdf(x, 1, be))
return priors
def __call__(self):
import sys
return getStandardPriors(sys.argv[1], sys.argv[2])
def setBorders(data,options):
"""
automatically set borders on the parameters based on were you sampled.
function Borders=setBorders(data,options)
this function sets borders on the parameter values of a given function
automaically
It sets: -the threshold to be within the range of the data +/- 50%
-the width to half the distance of two datapoints up to 10 times
the range of the data
-the lapse rate to 0 to .5
-the lower asymptote to 0 to .5 or fix to 1/n for nAFC
-the varscale to the full range from almost 0 to almost 1
"""
widthmin = options['widthmin']
# lapse fix to 0 - .5
lapseB = np.array([0,.5])
if options['expType'] == 'nAFC':
gammaB = np.array([1/options['expN'], 1/options['expN']])
elif options['expType'] == 'YesNo':
gammaB = np.array([0, .5])
elif options['expType'] == 'equalAsymptote':
gammaB = np.array([np.nan, np.nan])
# varscale from 0 to 1, 1 excluded!
varscaleB = np.array([0, 1-np.exp(-20)])
# if range was not given take from data
'''if options['stimulusRange'].size <= 1 :
options['stimulusRange'] = np.array([min(data[:,0]), max(data[:,0])])
stimRangeSet = False
else:
stimRangeSet= True
if options['logspace']:
options['stimulusRange'] = np.log(options['stimulusRange'])
'''
'''
We then assume it is one of the reparameterized functions with
alpha=threshold and beta= width
The threshold is assumed to be within the range of the data +/-
.5 times it's spread
'''
dataspread = np.diff(options['stimulusRange'])
alphaB = np.array([options['stimulusRange'][0] - .5*dataspread, options['stimulusRange'][1] +.5*dataspread]).squeeze()
''' the width we assume to be between half the minimal distance of
two points and 5 times the spread of the data
if len(np.unique(data[:,0])) > 1 and not(stimRangeSet):
widthmin = np.min(np.diff(np.sort(np.unique(data[:,0]))))
else :
widthmin = 100*np.spacing(options['stimulusRange'][1])
'''
''' We use the same prior as we previously used... e.g. we use the factor by
which they differ for the cumulative normal function '''
Cfactor = (my_norminv(.95,0,1) - my_norminv(.05, 0,1))/(my_norminv(1- options['widthalpha'], 0,1) - my_norminv(options['widthalpha'], 0,1))
betaB = np.array([widthmin, 3/Cfactor*dataspread])
borders =[[alphaB], [betaB], [lapseB], [gammaB], [varscaleB]]
borders = np.array(borders).squeeze()
return borders
def plotPrior(result,
lineWidth = 2,
lineColor = np.array([0,105,170])/255,
markerSize = 30):
"""
This function creates the plot illustrating the priors on the different
parameters
"""
data = result['data']
if np.size(result['options']['stimulusRange']) <= 1:
result['options']['stimulusRange'] = np.array([min(data[:,0]), max(data[:,0])])
stimRangeSet = False
else:
stimRangeSet = True
stimRange = result['options']['stimulusRange']
r = stimRange[1] - stimRange[0]
# get borders for width
# minimum = minimal difference of two stimulus levels
if len(np.unique(data[:,0])) > 1 and not(stimRangeSet):
widthmin = min(np.diff(np.sort(np.unique(data[:,0]))))
else:
widthmin = 100*np.spacing(stimRange[1])
# maximum = spread of the data
# We use the same prior as we previously used... e.g. we use the factor by
# which they differ for the cumulative normal function
Cfactor = (my_norminv(.95,0,1) - my_norminv(.05,0,1))/ \
(my_norminv(1-result['options']['widthalpha'], 0,1) - \
my_norminv(result['options']['widthalpha'], 0,1))
widthmax = r
steps = 10000
theta = np.empty(5)
for itheta in range(0,5):
if itheta == 0:
x = np.linspace(stimRange[0]-.5*r, stimRange[1]+.5*r, steps)
elif itheta == 1:
x = np.linspace(min(result['X1D'][itheta]), max(result['X1D'][1],),steps)
elif itheta == 2:
x = np.linspace(0,.5,steps)
elif itheta == 3:
x = np.linspace(0,.5,steps)
elif itheta == 4:
x = np.linspace(0,1,steps)
y = result['options']['priors'][itheta](x)
theta[itheta] = np.sum(x*y)/np.sum(y)
if result['options']['expType'] == 'equalAsymptote':
theta[3] = theta[2]
if result['options']['expType'] == 'nAFC':
theta[3] = 1/result['options']['expN']
# get limits for the psychometric function plots
xLimit = [stimRange[0] - .5*r , stimRange[1] +.5*r]
""" threshold """
xthresh = np.linspace(xLimit[0], xLimit[1], steps )
ythresh = result['options']['priors'][0](xthresh)
wthresh = convn(np.diff(xthresh), .5*np.array([1,1]))
cthresh = np.cumsum(ythresh*wthresh)
plt.subplot(2,3,1)
plt.plot(xthresh,ythresh, lw = lineWidth, c= lineColor)
plt.hold(True)
plt.xlim(xLimit)
plt.title('Threshold', fontsize = 18)
plt.ylabel('Density', fontsize = 18)
plt.subplot(2,3,4)
plt.plot(data[:,0], np.zeros(data[:,0].shape), 'k.', ms = markerSize*.75 )
plt.hold(True)
plt.ylabel('Percent Correct', fontsize = 18)
plt.xlim(xLimit)
for idot in range(0,5):
if idot == 0:
xcurrent = theta[0]
color = 'k'
elif idot == 1:
xcurrent = min(xthresh)
color = [1,200/255,0]
elif idot == 2:
tix = cthresh[cthresh >=.25].size
xcurrent = xthresh[-tix]
color = 'r'
elif idot == 3:
tix = cthresh[cthresh >= .75].size
xcurrent = xthresh[-tix]
color = 'b'
elif idot == 4:
xcurrent = max(xthresh)
color = 'g'
y = 100*(theta[3]+(1-theta[2])-theta[3])*result['options']['sigmoidHandle'](x,xcurrent, theta[1])
plt.subplot(2,3,4)
plt.plot(x,y, '-', lw=lineWidth,c=color )
plt.subplot(2,3,1)
plt.plot(xcurrent, result['options']['priors'][0](xcurrent), '.',c=color, ms = markerSize)
""" width"""
xwidth = np.linspace(widthmin, 3/Cfactor*widthmax, steps)
ywidth = result['options']['priors'][1](xwidth)
wwidth = convn(np.diff(xwidth), .5*np.array([1,1]))
cwidth = np.cumsum(ywidth*wwidth)
plt.subplot(2,3,2)
plt.plot(xwidth,ywidth,lw=lineWidth,c=lineColor)
plt.hold(True)
plt.xlim([widthmin,3/Cfactor*widthmax])
plt.title('Width',fontsize=18)
plt.subplot(2,3,5)
plt.plot(data[:,0],np.zeros(data[:,0].size),'k.',ms =markerSize*.75)
plt.hold(True)
plt.xlim(xLimit)
plt.xlabel('Stimulus Level',fontsize=18)
x = np.linspace(xLimit[0],xLimit[1],steps)
for idot in range(0,5):
if idot == 0:
xcurrent = theta[1]
color = 'k'
elif idot == 1:
xcurrent = min(xwidth)
color = [1,200/255,0]
elif idot == 2:
wix = cwidth[cwidth >= .25].size
xcurrent = xwidth[-wix]
color = 'r'
elif idot == 3:
wix = cwidth[cwidth >= .75].size
xcurrent = xwidth[-wix]
color = 'b'
elif idot ==4:
xcurrent = max(xwidth)
color = 'g'
y = 100*(theta[3]+ (1-theta[2] -theta[3])* result['options']['sigmoidHandle'](x,theta[0],xcurrent))
plt.subplot(2,3,5)
plt.plot(x,y,'-',lw = lineWidth, c= color)
plt.subplot(2,3,2)
plt.plot(xcurrent,result['options']['priors'][1](xcurrent),'.',c = color,ms=markerSize)
""" lapse """
xlapse = np.linspace(0,.5,steps)
ylapse = result['options']['priors'][2](xlapse)
wlapse = convn(np.diff(xlapse),.5*np.array([1,1]))
clapse = np.cumsum(ylapse*wlapse)
plt.subplot(2,3,3)
plt.plot(xlapse,ylapse,lw=lineWidth,c=lineColor)
plt.hold(True)
plt.xlim([0,.5])
plt.title('\lambda',fontsize=18)
plt.subplot(2,3,6)
plt.plot(data[:,0],np.zeros(data[:,0].size),'k.',ms=markerSize*.75)
plt.hold(True)
plt.xlim(xLimit)
x = np.linspace(xLimit[0],xLimit[1],steps)
for idot in range(0,5):
if idot == 0:
xcurrent = theta[2]
color = 'k'
elif idot == 1:
xcurrent = 0
color = [1,200/255,0]
elif idot == 2:
lix = clapse[clapse >= .25].size
xcurrent = xlapse[-lix]
color = 'r'
elif idot == 3:
lix = clapse[clapse >= .75].size
xcurrent = xlapse[-lix]
color = 'b'
elif idot ==4:
xcurrent = .5
color = 'g'
y = 100*(theta[3]+ (1-xcurrent-theta[3])*result['options']['sigmoidHandle'](x,theta[0],theta[1]))
plt.subplot(2,3,6)
plt.plot(x,y,'-',lw=lineWidth,c=color)
plt.subplot(2,3,3)
plt.plot(xcurrent,result['options']['priors'][2](xcurrent),'.',c=color,ms=markerSize)
a_handle = plt.gca()
a_handle.set_position([200,300,1000,600])
fig, ax = plt.subplots()
for item in [fig, ax]:
item.patch.set_visible(False)
if __name__ == "__main__":
result = {}
result['Fit'] = np.array([.004651, .004658, 1.7125E-7, .5, 1.0632E-4])
options = {}
options['expType'] = 'nAFC'
options['expN'] = 2
options['logspace'] = False
options['threshPC'] = .5
from utils import my_normcdf
alpha = .05
C = my_norminv(1-alpha,0,1)-my_norminv(alpha,0,1)
options['sigmoidHandle'] = lambda X,m,width: my_normcdf(X, (m-my_norminv(.5,0,width/C)), width/C)
tmp1 = np.array([10,15,20,25,30,35,40,45,50,60,70,80,100], dtype=float)/10000
tmp2 = np.array([45,50,44,44,52,53,62,64,76,79,88,90,90], dtype=float)
tmp3 = np.array([90 for i in range(len(tmp1))], dtype=float)
data = np.array([tmp1,tmp2,tmp3]).T
result['data'] = data
options['stimulusRange'] = 0
options['widthalpha'] = .05
options['betaPrior'] = 10
options['priors'] = [lambda x: [74.074074196287796 for i in range(len(x))]]
result['options'] = options
CIs = np.zeros((5,2,3))
def setBorders(data,options):
"""
automatically set borders on the parameters based on were you sampled.
function Borders=setBorders(data,options)
this function sets borders on the parameter values of a given function
automaically
It sets: -the threshold to be within the range of the data +/- 50%
-the width to half the distance of two datapoints up to 10 times
the range of the data
-the lapse rate to 0 to .5
-the lower asymptote to 0 to .5 or fix to 1/n for nAFC
-the varscale to the full range from almost 0 to almost 1
"""
widthmin = options['widthmin']
# lapse fix to 0 - .5
lapseB = np.array([0,.5])
if options['expType'] == 'nAFC':
gammaB = np.array([1/options['expN'], 1/options['expN']])
elif options['expType'] == 'YesNo':
gammaB = np.array([0, .5])
elif options['expType'] == 'equalAsymptote':
gammaB = np.array([np.nan, np.nan])
# varscale from 0 to 1, 1 excluded!
varscaleB = np.array([0, 1-np.exp(-20)])
# if range was not given take from data
'''if options['stimulusRange'].size <= 1 :
options['stimulusRange'] = np.array([min(data[:,0]), max(data[:,0])])
stimRangeSet = False
else:
stimRangeSet= True
if options['logspace']:
options['stimulusRange'] = np.log(options['stimulusRange'])
'''
'''
We then assume it is one of the reparameterized functions with
alpha=threshold and beta= width
The threshold is assumed to be within the range of the data +/-
.5 times it's spread
'''
dataspread = np.diff(options['stimulusRange'])
alphaB = np.array([options['stimulusRange'][0] - .5*dataspread, options['stimulusRange'][1] +.5*dataspread]).squeeze()
''' the width we assume to be between half the minimal distance of
two points and 5 times the spread of the data
if len(np.unique(data[:,0])) > 1 and not(stimRangeSet):
widthmin = np.min(np.diff(np.sort(np.unique(data[:,0]))))
else :
widthmin = 100*np.spacing(options['stimulusRange'][1])
'''
''' We use the same prior as we previously used... e.g. we use the factor by
which they differ for the cumulative normal function '''
Cfactor = (my_norminv(.95,0,1) - my_norminv(.05, 0,1))/(my_norminv(1- options['widthalpha'], 0,1) - my_norminv(options['widthalpha'], 0,1))
betaB = np.array([widthmin, 3/Cfactor*dataspread])
borders =[[alphaB], [betaB], [lapseB], [gammaB], [varscaleB]]
borders = np.array(borders).squeeze()
return borders
def plotPrior(result,
lineWidth=2,
lineColor=np.array([0, 105, 170]) / 255,
markerSize=30,
showImediate=True):
"""
This function creates the plot illustrating the priors on the different
parameters
"""
data = result['data']
if np.size(result['options']['stimulusRange']) <= 1:
result['options']['stimulusRange'] = np.array(
[min(data[:, 0]), max(data[:, 0])])
stimRangeSet = False
else:
stimRangeSet = True
stimRange = result['options']['stimulusRange']
r = stimRange[1] - stimRange[0]
# get borders for width
# minimum = minimal difference of two stimulus levels
if len(np.unique(data[:, 0])) > 1 and not (stimRangeSet):
widthmin = min(np.diff(np.sort(np.unique(data[:, 0]))))
else:
widthmin = 100 * np.spacing(stimRange[1])
# maximum = spread of the data
# We use the same prior as we previously used... e.g. we use the factor by
# which they differ for the cumulative normal function
Cfactor = (_utils.my_norminv(.95,0,1) - _utils.my_norminv(.05,0,1))/ \
(_utils.my_norminv(1-result['options']['widthalpha'], 0,1) - \
_utils.my_norminv(result['options']['widthalpha'], 0,1))
widthmax = r
steps = 10000
theta = np.empty(5)
for itheta in range(0, 5):
if itheta == 0:
x = np.linspace(stimRange[0] - .5 * r, stimRange[1] + .5 * r,
steps)
elif itheta == 1:
x = np.linspace(min(result['X1D'][itheta]),
max(result['X1D'][1], ), steps)
elif itheta == 2:
x = np.linspace(0, .5, steps)
elif itheta == 3:
x = np.linspace(0, .5, steps)
elif itheta == 4:
x = np.linspace(0, 1, steps)
y = result['options']['priors'][itheta](x)
theta[itheta] = np.sum(x * y) / np.sum(y)
if result['options']['expType'] == 'equalAsymptote':
theta[3] = theta[2]
if result['options']['expType'] == 'nAFC':
theta[3] = 1 / result['options']['expN']
# get limits for the psychometric function plots
xLimit = [stimRange[0] - .5 * r, stimRange[1] + .5 * r]
""" threshold """
xthresh = np.linspace(xLimit[0], xLimit[1], steps)
ythresh = result['options']['priors'][0](xthresh)
wthresh = _convn(np.diff(xthresh), .5 * np.array([1, 1]))
cthresh = np.cumsum(ythresh * wthresh)
plt.subplot(2, 3, 1)
plt.plot(xthresh, ythresh, lw=lineWidth, c=lineColor)
plt.hold(True)
plt.xlim(xLimit)
plt.title('Threshold', fontsize=18)
plt.ylabel('Density', fontsize=18)
plt.subplot(2, 3, 4)
plt.plot(data[:, 0], np.zeros(data[:, 0].shape), 'k.', ms=markerSize * .75)
plt.hold(True)
plt.ylabel('Percent Correct', fontsize=18)
plt.xlim(xLimit)
x = np.linspace(xLimit[0], xLimit[1], steps)
for idot in range(0, 5):
if idot == 0:
xcurrent = theta[0]
color = 'k'
elif idot == 1:
xcurrent = min(xthresh)
color = [1, 200 / 255, 0]
elif idot == 2:
tix = cthresh[cthresh >= .25].size
xcurrent = xthresh[-tix]
color = 'r'
elif idot == 3:
tix = cthresh[cthresh >= .75].size
xcurrent = xthresh[-tix]
color = 'b'
elif idot == 4:
xcurrent = max(xthresh)
color = 'g'
y = 100 * (theta[3] + ((1 - theta[2]) - theta[3]) *
result['options']['sigmoidHandle'](x, xcurrent, theta[1]))
plt.subplot(2, 3, 4)
plt.plot(x, y, '-', lw=lineWidth, c=color)
plt.subplot(2, 3, 1)
plt.plot(xcurrent,
result['options']['priors'][0](xcurrent),
'.',
c=color,
ms=markerSize)
""" width"""
xwidth = np.linspace(widthmin, 3 / Cfactor * widthmax, steps)
ywidth = result['options']['priors'][1](xwidth)
wwidth = _convn(np.diff(xwidth), .5 * np.array([1, 1]))
cwidth = np.cumsum(ywidth * wwidth)
plt.subplot(2, 3, 2)
plt.plot(xwidth, ywidth, lw=lineWidth, c=lineColor)
plt.hold(True)
plt.xlim([widthmin, 3 / Cfactor * widthmax])
plt.title('Width', fontsize=18)
plt.subplot(2, 3, 5)
plt.plot(data[:, 0], np.zeros(data[:, 0].size), 'k.', ms=markerSize * .75)
plt.hold(True)
plt.xlim(xLimit)
plt.xlabel('Stimulus Level', fontsize=18)
x = np.linspace(xLimit[0], xLimit[1], steps)
for idot in range(0, 5):
if idot == 0:
xcurrent = theta[1]
color = 'k'
elif idot == 1:
xcurrent = min(xwidth)
color = [1, 200 / 255, 0]
elif idot == 2:
wix = cwidth[cwidth >= .25].size
xcurrent = xwidth[-wix]
color = 'r'
elif idot == 3:
wix = cwidth[cwidth >= .75].size
xcurrent = xwidth[-wix]
color = 'b'
elif idot == 4:
xcurrent = max(xwidth)
color = 'g'
y = 100 * (theta[3] + (1 - theta[2] - theta[3]) *
result['options']['sigmoidHandle'](x, theta[0], xcurrent))
plt.subplot(2, 3, 5)
plt.plot(x, y, '-', lw=lineWidth, c=color)
plt.subplot(2, 3, 2)
plt.plot(xcurrent,
result['options']['priors'][1](xcurrent),
'.',
c=color,
ms=markerSize)
""" lapse """
xlapse = np.linspace(0, .5, steps)
ylapse = result['options']['priors'][2](xlapse)
wlapse = _convn(np.diff(xlapse), .5 * np.array([1, 1]))
clapse = np.cumsum(ylapse * wlapse)
plt.subplot(2, 3, 3)
plt.plot(xlapse, ylapse, lw=lineWidth, c=lineColor)
plt.hold(True)
plt.xlim([0, .5])
plt.title('\lambda', fontsize=18)
plt.subplot(2, 3, 6)
plt.plot(data[:, 0], np.zeros(data[:, 0].size), 'k.', ms=markerSize * .75)
plt.hold(True)
plt.xlim(xLimit)
x = np.linspace(xLimit[0], xLimit[1], steps)
for idot in range(0, 5):
if idot == 0:
xcurrent = theta[2]
color = 'k'
elif idot == 1:
xcurrent = 0
color = [1, 200 / 255, 0]
elif idot == 2:
lix = clapse[clapse >= .25].size
xcurrent = xlapse[-lix]
color = 'r'
elif idot == 3:
lix = clapse[clapse >= .75].size
xcurrent = xlapse[-lix]
color = 'b'
elif idot == 4:
xcurrent = .5
color = 'g'
y = 100 * (theta[3] + (1 - xcurrent - theta[3]) *
result['options']['sigmoidHandle'](x, theta[0], theta[1]))
plt.subplot(2, 3, 6)
plt.plot(x, y, '-', lw=lineWidth, c=color)
plt.subplot(2, 3, 3)
plt.plot(np.array(xcurrent),
result['options']['priors'][2](np.array(xcurrent)),
'.',
c=color,
ms=markerSize)
if (showImediate):
plt.show()
