Example #1
0
    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
Example #2
0
    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
Example #3
0
        """

        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:

"""
Example #4
0
        """

        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
Example #5
0
         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)