def confidence_interval(self):
"""The size of the 1-alpha confidence interval"""
coh_var = np.zeros(
(self.input.data.shape[0], self.input.data.shape[0], self._L), 'd')
for i in range(self.input.data.shape[0]):
for j in range(i):
if i != j:
coh_var[i, j] = tsu.jackknifed_coh_variance(
self.spectra[i],
self.spectra[j],
self.eigs,
adaptive=self._adaptive)
idx = triu_indices(self.input.data.shape[0], 1)
coh_var[idx[0], idx[1], ...] = coh_var[idx[1], idx[0], ...].conj()
coh_mat_xform = tsu.normalize_coherence(self.coherence,
2 * self.df - 2)
lb = coh_mat_xform + dist.t.ppf(self.alpha / 2,
self.df - 1) * np.sqrt(coh_var)
ub = coh_mat_xform + dist.t.ppf(1 - self.alpha / 2,
self.df - 1) * np.sqrt(coh_var)
# convert this measure with the normalizing function
tsu.normal_coherence_to_unit(lb, 2 * self.df - 2, lb)
tsu.normal_coherence_to_unit(ub, 2 * self.df - 2, ub)
return ub - lb
def confidence_interval(self):
"""The size of the 1-alpha confidence interval"""
coh_var = np.zeros((self.input.data.shape[0],
self.input.data.shape[0],
self._L), 'd')
for i in range(self.input.data.shape[0]):
for j in range(i):
if i != j:
coh_var[i, j] = tsu.jackknifed_coh_variance(
self.spectra[i],
self.spectra[j],
self.eigs,
adaptive=self._adaptive
)
idx = triu_indices(self.input.data.shape[0], 1)
coh_var[idx[0], idx[1], ...] = coh_var[idx[1], idx[0], ...].conj()
coh_mat_xform = tsu.normalize_coherence(self.coherence,
2 * self.df - 2)
lb = coh_mat_xform + dist.t.ppf(self.alpha / 2,
self.df - 1) * np.sqrt(coh_var)
ub = coh_mat_xform + dist.t.ppf(1 - self.alpha / 2,
self.df - 1) * np.sqrt(coh_var)
# convert this measure with the normalizing function
tsu.normal_coherence_to_unit(lb, 2 * self.df - 2, lb)
tsu.normal_coherence_to_unit(ub, 2 * self.df - 2, ub)
return ub - lb
"""
coh_mat[i, j] = np.abs(sxy)**2
coh_mat[i, j] /= (sxx * syy)
csd_mat[i, j] = sxy
"""
The variance from the different samples is calculated using a jack-knife
approach:
"""
if i != j:
coh_var[i, j] = utils.jackknifed_coh_variance(
tspectra[i],
tspectra[j],
eigs,
adaptive=True,
)
"""
This measure is normalized, based on the number of tapers:
"""
coh_mat_xform = utils.normalize_coherence(coh_mat, 2 * K - 2)
"""
We calculate 95% confidence intervals based on the jack-knife variance
calculation:
"""
"""
coh_mat[i, j] = np.abs(sxy) ** 2
coh_mat[i, j] /= (sxx * syy)
csd_mat[i, j] = sxy
"""
The variance from the different samples is calculated using a jack-knife
approach:
"""
if i != j:
coh_var[i, j] = utils.jackknifed_coh_variance(
tspectra[i], tspectra[j], eigs, adaptive=True,
)
"""
This measure is normalized, based on the number of tapers:
"""
coh_mat_xform = utils.normalize_coherence(coh_mat, 2 * K - 2)
"""
We calculate 95% confidence intervals based on the jack-knife variance
tspectra[i], tspectra[j], (w[i], w[j]), sides='onesided'
)
sxx = alg.mtm_cross_spectrum(
tspectra[i], tspectra[i], (w[i], w[i]), sides='onesided'
).real
syy = alg.mtm_cross_spectrum(
tspectra[j], tspectra[j], (w[i], w[j]), sides='onesided'
).real
psd_mat[0,i,j] = sxx
psd_mat[1,i,j] = syy
coh_mat[i,j] = np.abs(sxy)**2
coh_mat[i,j] /= (sxx * syy)
csd_mat[i,j] = sxy
if i != j:
coh_var[i,j] = utils.jackknifed_coh_variance(
tspectra[i], tspectra[j], weights=(w[i], w[j]), last_freq=L
)
upper_idc = utils.triu_indices(nseq, k=1)
lower_idc = utils.tril_indices(nseq, k=-1)
coh_mat[upper_idc] = coh_mat[lower_idc]
coh_var[upper_idc] = coh_var[lower_idc]
# convert this measure with the normalizing function
coh_mat_xform = utils.normalize_coherence(coh_mat, 2*K-2)
t025_limit = coh_mat_xform + dist.t.ppf(.025, K-1)*np.sqrt(coh_var)
t975_limit = coh_mat_xform + dist.t.ppf(.975, K-1)*np.sqrt(coh_var)
utils.normal_coherence_to_unit(t025_limit, 2*K-2, t025_limit)
utils.normal_coherence_to_unit(t975_limit, 2*K-2, t975_limit)