def altCDF(peaks, mu, sigma=None, exc=None, method="RFT"):
"""
Returns the CDF of the alternative peak distribution
Parameters
----------
peaks : :obj:`numpy.ndarray`
List of peak heights (z-values).
mu : :obj:`float`
Mean from fitted normal distribution.
sigma : :obj:`float`
Standard deviation from fitted normal distribution.
exc : :obj:`float`, optional
Z-threshold (excursion threshold)
method : {'RFT', 'CS'}, optional
Multiple comparisons correction method.
Returns
-------
Fa : :obj:`numpy.ndarray`
Cumulative density of the peak heights under Ha.
"""
peaks = np.asarray(peaks)
if method == 'RFT':
ksi = (peaks - mu) / sigma
alpha = (exc - mu) / sigma
Fa = (norm.cdf(ksi) - norm.cdf(alpha)) / (1 - norm.cdf(alpha))
elif method == 'CS':
Fa = np.array([
integrate.quad(lambda x: peakdistribution.peakdens3D(x, 1), -20,
y)[0] for y in peaks - mu
])
else:
raise ValueError('Argument `method` must be either "RFT" or "CS"')
return Fa
def altPDF(peaks,mu,sigma=None,exc=None,method="RFT"): """ altPDF: Returns probability density using a truncated normal distribution that we define as the distribution of local maxima in a GRF under the alternative hypothesis of activation parameters ---------- peaks: float or list of floats list of peak heigths mu: sigma: returns ------- fa: float or list probability density of the peaks heights under Ha """ #Returns probability density of the alternative peak distribution peaks = np.asarray(peaks) if method == "RFT": # assert type(sigma) is in [float, int] # assert sigma is not None ksi = (peaks-mu)/sigma alpha = (exc-mu)/sigma num = 1/sigma * scipy.stats.norm.pdf(ksi) den = 1. - scipy.stats.norm.cdf(alpha) fa = num/den elif method == "CS": fa = [peakdistribution.peakdens3D(y-mu,1) for y in peaks] return fa
def nulPDF(peaks, exc=None, method='RFT'):
"""
Returns probability density of the null peak distribution.
Parameters
----------
peaks : :obj:`numpy.ndarray`
List of peak heights (z-values).
exc : :obj:`float`, optional
Z-threshold (excursion threshold)
method : {'RFT', 'CS'}, optional
Multiple comparisons correction method.
Returns
-------
f0 : :obj:`numpy.ndarray`
Probability density of the peaks heights under H0.
"""
peaks = np.asarray(peaks)
if method == 'RFT':
f0 = exc * np.exp(-exc * (peaks - exc))
elif method == 'CS':
f0 = np.array([peakdistribution.peakdens3D(x, 1) for x in peaks])
else:
raise ValueError('Argument `method` must be either "RFT" or "CS"')
return f0
def _nulCDF(peaks, exc=None, method='RFT'):
"""
Returns the CDF of the null peak distribution.
Parameters
----------
peaks : :obj:`numpy.ndarray`
List of peak heights (z-values).
exc : :obj:`float`, optional
Z-threshold (excursion threshold)
method : {'RFT', 'CS'}, optional
Multiple comparisons correction method.
Returns
-------
F0 : :obj:`numpy.ndarray`
Cumulative density of the peak heights under H0.
"""
peaks = np.asarray(peaks)
if method == "RFT":
F0 = 1 - np.exp(-exc * (peaks - exc))
elif method == "CS":
F0 = np.array([
integrate.quad(lambda x: peakdistribution.peakdens3D(x, 1), -20,
y)[0] for y in peaks
])
else:
raise ValueError('Argument `method` must be either "RFT" or "CS"')
return F0
def altPDF(peaks, mu, sigma=None, exc=None, method="RFT"):
"""
altPDF: Returns probability density using a truncated normal
distribution that we define as the distribution of local maxima in a
GRF under the alternative hypothesis of activation
parameters
----------
peaks: float or list of floats
list of peak heigths
mu:
sigma:
returns
-------
fa: float or list
probability density of the peaks heights under Ha
"""
#Returns probability density of the alternative peak distribution
peaks = np.asarray(peaks)
if method == "RFT":
# assert type(sigma) is in [float, int]
# assert sigma is not None
ksi = (peaks - mu) / sigma
alpha = (exc - mu) / sigma
num = 1 / sigma * scipy.stats.norm.pdf(ksi)
den = 1. - scipy.stats.norm.cdf(alpha)
fa = num / den
elif method == "CS":
fa = [peakdistribution.peakdens3D(y - mu, 1) for y in peaks]
return fa
def nulCDF(peaks,exc=None,method="RFT"): # Returns the CDF of the null peak distribution peaks = np.asarray(peaks) if method == "RFT": F0 = 1-np.exp(-exc*(peaks-exc)) elif method == "CS": F0 = [integrate.quad(lambda x:peakdistribution.peakdens3D(x,1),-20,y)[0] for y in peaks] return F0
def nulPDF(peaks,exc=None,method="RFT"): #Returns probability density of the null peak distribution peaks = np.asarray(peaks) if method == "RFT": f0 = exc*np.exp(-exc*(peaks-exc)) elif method == "CS": f0 = [peakdistribution.peakdens3D(x,1) for x in peaks] return f0
def nulPDF(peaks, exc=None, method="RFT"):
#Returns probability density of the null peak distribution
peaks = np.asarray(peaks)
if method == "RFT":
f0 = exc * np.exp(-exc * (peaks - exc))
elif method == "CS":
f0 = [peakdistribution.peakdens3D(x, 1) for x in peaks]
return f0
def altCDF(peaks,mu,sigma=None,exc=None,method="RFT"): # Returns the CDF of the alternative peak distribution peaks = np.asarray(peaks) if method == "RFT": ksi = (peaks-mu)/sigma alpha = (exc-mu)/sigma Fa = (scipy.stats.norm.cdf(ksi) - scipy.stats.norm.cdf(alpha))/(1-scipy.stats.norm.cdf(alpha)) elif method == "CS": Fa = [integrate.quad(lambda x:peakdistribution.peakdens3D(x,1),-20,y)[0] for y in peaks-mu] return Fa
def nulCDF(peaks, exc=None, method="RFT"):
# Returns the CDF of the null peak distribution
peaks = np.asarray(peaks)
if method == "RFT":
F0 = 1 - np.exp(-exc * (peaks - exc))
elif method == "CS":
F0 = [
integrate.quad(lambda x: peakdistribution.peakdens3D(x, 1), -20,
y)[0] for y in peaks
]
return F0
def altCDF(peaks, mu, sigma=None, exc=None, method="RFT"):
# Returns the CDF of the alternative peak distribution
peaks = np.asarray(peaks)
if method == "RFT":
ksi = (peaks - mu) / sigma
alpha = (exc - mu) / sigma
Fa = (scipy.stats.norm.cdf(ksi) -
scipy.stats.norm.cdf(alpha)) / (1 - scipy.stats.norm.cdf(alpha))
elif method == "CS":
Fa = [
integrate.quad(lambda x: peakdistribution.peakdens3D(x, 1), -20,
y)[0] for y in peaks - mu
]
return Fa
def altPDF(peaks, mu, sigma=None, exc=None, method='RFT'):
"""
Returns probability density using a truncated normal distribution that we
define as the distribution of local maxima in a GRF under the alternative
hypothesis of activation.
Parameters
----------
peaks : :obj:`numpy.ndarray`
List of peak heights (z-values).
mu : :obj:`float`
Mean from fitted normal distribution.
sigma : :obj:`float`
Standard deviation from fitted normal distribution.
exc : :obj:`float`, optional
Z-threshold (excursion threshold)
method : {'RFT', 'CS'}, optional
Multiple comparisons correction method.
Returns
-------
fa : :obj:`numpy.ndarray`
Probability density of the peaks heights under Ha.
"""
# Returns probability density of the alternative peak distribution
peaks = np.asarray(peaks)
if method == 'RFT':
ksi = (peaks - mu) / sigma
alpha = (exc - mu) / sigma
num = 1. / sigma * norm.pdf(ksi)
den = 1. - norm.cdf(alpha)
fa = num / den
elif method == 'CS':
fa = np.array([peakdistribution.peakdens3D(y - mu, 1) for y in peaks])
else:
raise ValueError('Argument `method` must be either "RFT" or "CS"')
return fa
def test_peakdistribution(self):
x = peakdistribution.peakdens3D(2,1)
self.assertEqual(np.around(x,decimals=2),0.48)
def test_peakdistribution(self):
x = peakdistribution.peakdens3D(2, 1)
self.assertEqual(np.around(x, decimals=2), 0.48)
