def test_estimate_varatio(p=1.0e-04, sigma2=1):
# This is a random test, but is design to fail only rarely....
ntrial = 300
n = 10
random = np.zeros(10)
rsd = np.zeros(n)
sd = np.multiply.outer(np.linspace(0, 1, 40), np.ones(ntrial)) + np.ones(
(40, ntrial))
for i in range(n):
Y = np.random.standard_normal((40, ntrial)) * np.sqrt((sd**2 + sigma2))
results = onesample.estimate_varatio(Y, sd)
results = onesample.estimate_varatio(Y, sd)
random[i] = results['random'].mean()
rsd[i] = results['random'].std()
# Compute the mean just to be sure it works
W = 1. / (sd**2 + results['random'])
mu = onesample.estimate_mean(Y,
np.sqrt(sd**2 + results['random']))['effect']
yield assert_almost_equal, mu, (W * Y).sum(0) / W.sum(0)
rsd = np.sqrt((rsd**2).mean() / ntrial)
T = np.fabs((random.mean() - sigma2) / (rsd / np.sqrt(n)))
# should fail one in every 1/p trials at least for sigma > 0,
# small values of sigma seem to have some bias
if T > norm.ppf(1 - p / 2):
raise ValueError('large T value, but algorithm works, '
'could be a statistical failure')
def group_analysis(design, contrast):
""" Compute group analysis effect, t, sd for `design` and `contrast`
Saves to disk in 'group' analysis directory
Parameters
----------
design : {'block', 'event'}
contrast : str
contrast name
"""
array = np.array # shorthand
# Directory where output will be written
odir = futil.ensure_dir(futil.DATADIR, 'group', design, contrast)
# Which subjects have this (contrast, design) pair?
subj_con_dirs = futil.subj_des_con_dirs(design, contrast)
if len(subj_con_dirs) == 0:
raise ValueError('No subjects for %s, %s' % (design, contrast))
# Assemble effects and sds into 4D arrays
sds = []
Ys = []
for s in subj_con_dirs:
sd_img = load_image(pjoin(s, "sd.nii"))
effect_img = load_image(pjoin(s, "effect.nii"))
sds.append(sd_img.get_data())
Ys.append(effect_img.get_data())
sd = array(sds)
Y = array(Ys)
# This function estimates the ratio of the fixed effects variance
# (sum(1/sd**2, 0)) to the estimated random effects variance
# (sum(1/(sd+rvar)**2, 0)) where rvar is the random effects variance.
# The EM algorithm used is described in:
#
# Worsley, K.J., Liao, C., Aston, J., Petre, V., Duncan, G.H.,
# Morales, F., Evans, A.C. (2002). \'A general statistical
# analysis for fMRI data\'. NeuroImage, 15:1-15
varest = onesample.estimate_varatio(Y, sd)
random_var = varest['random']
# XXX - if we have a smoother, use
# random_var = varest['fixed'] * smooth(varest['ratio'])
# Having estimated the random effects variance (and possibly smoothed it),
# the corresponding estimate of the effect and its variance is computed and
# saved.
# This is the coordmap we will use
coordmap = futil.load_image_fiac("fiac_00","wanatomical.nii").coordmap
adjusted_var = sd**2 + random_var
adjusted_sd = np.sqrt(adjusted_var)
results = onesample.estimate_mean(Y, adjusted_sd)
for n in ['effect', 'sd', 't']:
im = api.Image(results[n], copy(coordmap))
save_image(im, pjoin(odir, "%s.nii" % n))
def group_analysis(design, contrast):
""" Compute group analysis effect, t, sd for `design` and `contrast`
Saves to disk in 'group' analysis directory
Parameters
----------
design : {'block', 'event'}
contrast : str
contrast name
"""
array = np.array # shorthand
# Directory where output will be written
odir = futil.ensure_dir(futil.DATADIR, 'group', design, contrast)
# Which subjects have this (contrast, design) pair?
subj_con_dirs = futil.subj_des_con_dirs(design, contrast)
if len(subj_con_dirs) == 0:
raise ValueError('No subjects for %s, %s' % (design, contrast))
# Assemble effects and sds into 4D arrays
sds = []
Ys = []
for s in subj_con_dirs:
sd_img = load_image(pjoin(s, "sd.nii"))
effect_img = load_image(pjoin(s, "effect.nii"))
sds.append(sd_img.get_data())
Ys.append(effect_img.get_data())
sd = array(sds)
Y = array(Ys)
# This function estimates the ratio of the fixed effects variance
# (sum(1/sd**2, 0)) to the estimated random effects variance
# (sum(1/(sd+rvar)**2, 0)) where rvar is the random effects variance.
# The EM algorithm used is described in:
#
# Worsley, K.J., Liao, C., Aston, J., Petre, V., Duncan, G.H.,
# Morales, F., Evans, A.C. (2002). \'A general statistical
# analysis for fMRI data\'. NeuroImage, 15:1-15
varest = onesample.estimate_varatio(Y, sd)
random_var = varest['random']
# XXX - if we have a smoother, use
# random_var = varest['fixed'] * smooth(varest['ratio'])
# Having estimated the random effects variance (and possibly smoothed it),
# the corresponding estimate of the effect and its variance is computed and
# saved.
# This is the coordmap we will use
coordmap = futil.load_image_ds105("fiac_00", "wanatomical.nii").coordmap
adjusted_var = sd**2 + random_var
adjusted_sd = np.sqrt(adjusted_var)
results = onesample.estimate_mean(Y, adjusted_sd)
for n in ['effect', 'sd', 't']:
im = api.Image(results[n], copy(coordmap))
save_image(im, pjoin(odir, "%s.nii" % n))
def group_analysis_signs(design, contrast, mask, signs=None):
"""
This function refits the EM model with a vector of signs.
Used in the permutation tests.
Returns the maximum of the T-statistic within mask
Parameters
----------
design: one of 'block', 'event'
contrast: str
mask: array-like
signs: ndarray, optional
Defaults to np.ones. Should have shape (*,nsubj)
where nsubj is the number of effects combined in the group analysis.
Returns
-------
minT: np.ndarray, minima of T statistic within mask, one for each
vector of signs
maxT: np.ndarray, maxima of T statistic within mask, one for each
vector of signs
"""
maska = np.asarray(mask).astype(np.bool)
# Which subjects have this (contrast, design) pair?
subjects = futil.subject_dirs(design, contrast)
sd = np.array([np.array(load_image(pjoin(s, "sd.nii")))[:,maska]
for s in subjects])
Y = np.array([np.array(load_image(pjoin(s, "effect.nii")))[:,maska]
for s in subjects])
if signs is None:
signs = np.ones((1, Y.shape[0]))
maxT = np.empty(signs.shape[0])
minT = np.empty(signs.shape[0])
for i, sign in enumerate(signs):
signY = sign[:,np.newaxis] * Y
varest = onesample.estimate_varatio(signY, sd)
random_var = varest['random']
adjusted_var = sd**2 + random_var
adjusted_sd = np.sqrt(adjusted_var)
results = onesample.estimate_mean(Y, adjusted_sd)
T = results['t']
minT[i], maxT[i] = np.nanmin(T), np.nanmax(T)
return minT, maxT
def test_estimate_varatio(p=1.0e-04, sigma2=1):
# This is a random test, but is design to fail only rarely....
ntrial = 300
n = 10
random = np.zeros(10)
rsd = np.zeros(n)
sd = np.multiply.outer(
np.linspace(0,1,40),
np.ones(ntrial)
) + np.ones((40,ntrial))
for i in range(n):
Y = np.random.standard_normal((40,ntrial)) * np.sqrt((sd**2 + sigma2))
results = onesample.estimate_varatio(Y, sd)
results = onesample.estimate_varatio(Y, sd)
random[i] = results['random'].mean()
rsd[i] = results['random'].std()
# Compute the mean just to be sure it works
W = 1. / (sd**2 + results['random'])
mu = onesample.estimate_mean(Y, np.sqrt(sd**2 + results['random']))['effect']
yield assert_almost_equal, mu, (W*Y).sum(0) / W.sum(0)
rsd = np.sqrt((rsd**2).mean() / ntrial)
T = np.fabs((random.mean() - sigma2) / (rsd / np.sqrt(n)))
# should fail one in every 1/p trials at least for sigma > 0,
# small values of sigma seem to have some bias
if T > norm.ppf(1-p/2):
raise ValueError('large T value, but algorithm works, '
'could be a statistical failure')
def group_analysis(design, contrast):
"""
Compute group analysis effect, sd and t
for a given contrast and design type
"""
array = np.array # shorthand
# Directory where output will be written
odir = futil.ensure_dir(futil.DATADIR, 'group', design, contrast)
# Which subjects have this (contrast, design) pair?
subjects = futil.subject_dirs(design, contrast)
sd = array([array(load_image(pjoin(s, "sd.nii"))) for s in subjects])
Y = array([array(load_image(pjoin(s, "effect.nii"))) for s in subjects])
# This function estimates the ratio of the
# fixed effects variance (sum(1/sd**2, 0))
# to the estimated random effects variance
# (sum(1/(sd+rvar)**2, 0)) where
# rvar is the random effects variance.
# The EM algorithm used is described in
#
# Worsley, K.J., Liao, C., Aston, J., Petre, V., Duncan, G.H.,
# Morales, F., Evans, A.C. (2002). \'A general statistical
# analysis for fMRI data\'. NeuroImage, 15:1-15
varest = onesample.estimate_varatio(Y, sd)
random_var = varest['random']
# XXX - if we have a smoother, use
# random_var = varest['fixed'] * smooth(varest['ratio'])
# Having estimated the random effects variance (and
# possibly smoothed it), the corresponding
# estimate of the effect and its variance is
# computed and saved.
# This is the coordmap we will use
coordmap = futil.load_image_fiac("fiac_00","wanatomical.nii").coordmap
adjusted_var = sd**2 + random_var
adjusted_sd = np.sqrt(adjusted_var)
results = onesample.estimate_mean(Y, adjusted_sd)
for n in ['effect', 'sd', 't']:
im = api.Image(results[n], coordmap.copy())
save_image(im, pjoin(odir, "%s.nii" % n))
def group_analysis_signs(design, contrast, mask, signs=None):
""" Refit the EM model with a vector of signs.
Used in the permutation tests.
Returns the maximum of the T-statistic within mask
Parameters
----------
design: one of 'block', 'event'
contrast: str
name of contrast to estimate
mask : ``Image`` instance or array-like
image containing mask, or array-like
signs: ndarray, optional
Defaults to np.ones. Should have shape (*,nsubj)
where nsubj is the number of effects combined in the group analysis.
Returns
-------
minT: np.ndarray, minima of T statistic within mask, one for each
vector of signs
maxT: np.ndarray, maxima of T statistic within mask, one for each
vector of signs
"""
if api.is_image(mask):
maska = mask.get_data()
else:
maska = np.asarray(mask)
maska = maska.astype(np.bool)
# Which subjects have this (contrast, design) pair?
subj_con_dirs = futil.subj_des_con_dirs(design, contrast)
# Assemble effects and sds into 4D arrays
sds = []
Ys = []
for s in subj_con_dirs:
sd_img = load_image(pjoin(s, "sd.nii"))
effect_img = load_image(pjoin(s, "effect.nii"))
sds.append(sd_img.get_data()[maska])
Ys.append(effect_img.get_data()[maska])
sd = np.array(sds)
Y = np.array(Ys)
if signs is None:
signs = np.ones((1, Y.shape[0]))
maxT = np.empty(signs.shape[0])
minT = np.empty(signs.shape[0])
for i, sign in enumerate(signs):
signY = sign[:,np.newaxis] * Y
varest = onesample.estimate_varatio(signY, sd)
random_var = varest['random']
adjusted_var = sd**2 + random_var
adjusted_sd = np.sqrt(adjusted_var)
results = onesample.estimate_mean(Y, adjusted_sd)
T = results['t']
minT[i], maxT[i] = np.nanmin(T), np.nanmax(T)
return minT, maxT
def group_analysis_signs(design, contrast, mask, signs=None):
""" Refit the EM model with a vector of signs.
Used in the permutation tests.
Returns the maximum of the T-statistic within mask
Parameters
----------
design: one of 'block', 'event'
contrast: str
name of contrast to estimate
mask : ``Image`` instance or array-like
image containing mask, or array-like
signs: ndarray, optional
Defaults to np.ones. Should have shape (*,nsubj)
where nsubj is the number of effects combined in the group analysis.
Returns
-------
minT: np.ndarray, minima of T statistic within mask, one for each
vector of signs
maxT: np.ndarray, maxima of T statistic within mask, one for each
vector of signs
"""
if api.is_image(mask):
maska = mask.get_data()
else:
maska = np.asarray(mask)
maska = maska.astype(np.bool)
# Which subjects have this (contrast, design) pair?
subj_con_dirs = futil.subj_des_con_dirs(design, contrast)
# Assemble effects and sds into 4D arrays
sds = []
Ys = []
for s in subj_con_dirs:
sd_img = load_image(pjoin(s, "sd.nii"))
effect_img = load_image(pjoin(s, "effect.nii"))
sds.append(sd_img.get_data()[maska])
Ys.append(effect_img.get_data()[maska])
sd = np.array(sds)
Y = np.array(Ys)
if signs is None:
signs = np.ones((1, Y.shape[0]))
maxT = np.empty(signs.shape[0])
minT = np.empty(signs.shape[0])
for i, sign in enumerate(signs):
signY = sign[:, np.newaxis] * Y
varest = onesample.estimate_varatio(signY, sd)
random_var = varest['random']
adjusted_var = sd**2 + random_var
adjusted_sd = np.sqrt(adjusted_var)
results = onesample.estimate_mean(Y, adjusted_sd)
T = results['t']
minT[i], maxT[i] = np.nanmin(T), np.nanmax(T)
return minT, maxT
