Python chi2.ppf方法代碼示例

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def  _ci_limits_var(self, var):
        """
        Used to determine the confidence intervals for the variance.
        It calls test_var and when called by an optimizer,
        finds the value of sig2_0 that is chi2.ppf(significance-level)

        Parameters
        ----------
        var_test : float
            Hypothesized value of the variance

        Returns
        -------
        diff : float
            The difference between the log likelihood ratio at var_test and a
            pre-specified value.
        """
        return self.test_var(var)[0] - self.r0 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def visualize_pruning(w_norm, n_retained,
                      title='Initial model weights vs theoretical for pruning'):
    fig, ax1 = plt.subplots()
    ax1.set_title(title)
    ax1.hist(w_norm, normed=True, bins=200, alpha=0.6, histtype='stepfilled',
             range=[0, n_retained * 5])
    ax1.axvline(x=n_retained, linewidth=1, color='r')
    ax1.set_ylabel('PDF', color='b')

    ax2 = ax1.twinx()
    ax2.set_ylabel('Survival Function', color='r')

    ax1.set_xlabel('w_norm')

    x = np.linspace(chi2.ppf(0.001, n_retained),
                    chi2.ppf(0.999, n_retained), 100)
    ax2.plot(x, chi2.sf(x, n_retained),
             'g-', lw=1, alpha=0.6, label='chi2 pdf')
    ax1.plot(x, chi2.pdf(x, n_retained),
             'r-', lw=1, alpha=0.6, label='chi2 pdf') 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def _fisher_confint(self, alpha: float, observed: bool = False) -> List[float]:
        """Compute the Fisher information confidence interval for the MLE of the previous run.

        Args:
            alpha: Specifies the (1 - alpha) confidence level (0 < alpha < 1).
            observed: If True, the observed Fisher information is used to construct the
                confidence interval, otherwise the expected Fisher information.

        Returns:
            The Fisher information confidence interval.
        """
        shots = self._ret['shots']
        mle = self._ret['ml_value']

        # approximate the standard deviation of the MLE and construct the confidence interval
        std = np.sqrt(shots * self._compute_fisher_information(observed))
        ci = mle + norm.ppf(1 - alpha / 2) / std * np.array([-1, 1])

        # transform the confidence interval from [0, 1] to the target interval
        return [self.a_factory.value_to_estimation(bound) for bound in ci] 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def _h_getMahalanobisRobust(dat, critical_alpha=0.01, good_rows=np.zeros(0)):
    '''Calculate the Mahalanobis distance from the sample vector.'''
    if good_rows.size == 0:
        good_rows = np.any(~np.isnan(dat), axis=1)

    try:
        dat2fit = dat[good_rows]
        assert not np.any(np.isnan(dat2fit))

        robust_cov = MinCovDet().fit(dat2fit)
        mahalanobis_dist = np.sqrt(robust_cov.mahalanobis(dat))
    except ValueError:
        # this step will fail if the covariance matrix is not singular. This happens if the data is not
        # a unimodal symetric distribution. For example there is too many small noisy particles. Therefore
        # I will take a safe option and return zeros in the mahalanobis
        # distance if this is the case.
        mahalanobis_dist = np.zeros(dat.shape[0])

    # critial distance of the maholanobis distance using the chi-square distirbution
    # https://en.wikiversity.org/wiki/Mahalanobis%27_distance
    # http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2.html
    maha_lim = chi2.ppf(1 - critical_alpha, dat.shape[1])
    outliers = mahalanobis_dist > maha_lim

    return mahalanobis_dist, outliers, maha_lim 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def chi2_cutoff(D, cutoff=3.):
    """D-dimensional eqiuvalent of "n sigma" cut.

    Evaluates the quantile function of the chi-squared distribution to determine
    the limit for the chi^2 of samples wrt to GMM so that they satisfy the
    68-95-99.7 percent rule of the 1D Normal distribution.

    Args:
        D (int): dimensions of the feature space
        cutoff (float): 1D equivalent cut [in units of sigma]

    Returns:
        float: upper limit for chi-squared in D dimensions
    """
    import scipy.stats
    cdf_1d = scipy.stats.norm.cdf(cutoff)
    confidence_1d = 1-(1-cdf_1d)*2
    cutoff_nd = scipy.stats.chi2.ppf(confidence_1d, D)
    return cutoff_nd 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def recover_spikes(self, vbParam, pca, maha_dist=1):
    
        N, D = pca.shape
        # Cat: TODO: check if this maha thresholding recovering distance is good
        threshold = np.sqrt(chi2.ppf(0.99, D))

        # update rhat on full data
        maskedData = mfm.maskData(pca[:,:,np.newaxis], np.ones([N, 1]), np.arange(N))
        vbParam.update_local(maskedData)

        # calculate mahalanobis distance
        maha = mfm.calc_mahalonobis(vbParam, pca[:,:,np.newaxis])
        idx_recovered = np.where(~np.all(maha >= threshold, axis=1))[0]
        vbParam.rhat = vbParam.rhat[idx_recovered]

        # zero out low assignment vals
        if True:
            vbParam.rhat[vbParam.rhat < self.assignment_delete_threshold] = 0
            vbParam.rhat = vbParam.rhat/np.sum(vbParam.rhat,
                                             1, keepdims=True)

        return idx_recovered, vbParam 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def get_robust_scaling(scale_typ, model, ds, circuitList, parameters, evaltree_cache, comm, memLimit):
    """
    Get the per-circuit data scaling ("weights") for a given type of robust-data-scaling.
    TODO: docstring - more details
    """

    fitQty = _get_fit_qty(model, ds, circuitList, parameters, evaltree_cache, comm, memLimit)
    #Note: fitQty[iCircuit] gives fit quantity for a single circuit, aggregated over outcomes.

    expected = (len(ds.get_outcome_labels()) - 1)  # == "k"
    dof_per_box = expected; nboxes = len(circuitList)
    pc = 0.05  # hardcoded (1 - confidence level) for now -- make into advanced option w/default

    circuitWeights = {}
    if scale_typ in ("robust", "Robust"):
        # Robust scaling V1: drastically scale down weights of especially bad sequences
        threshold = _np.ceil(_chi2.ppf(1 - pc / nboxes, dof_per_box))
        for i, opstr in enumerate(circuitList):
            if fitQty[i] > threshold:
                circuitWeights[opstr] = expected / fitQty[i]  # scaling factor

    elif scale_typ in ("robust+", "Robust+"):
        # Robust scaling V2: V1 + rescale to desired chi2 distribution without reordering
        threshold = _np.ceil(_chi2.ppf(1 - pc / nboxes, dof_per_box))
        scaled_fitQty = fitQty.copy()
        for i, opstr in enumerate(circuitList):
            if fitQty[i] > threshold:
                circuitWeights[opstr] = expected / fitQty[i]  # scaling factor
                scaled_fitQty[i] = expected  # (fitQty[i]*circuitWeights[opstr])

        N = len(fitQty)
        percentiles = [_chi2.ppf((i + 1) / (N + 1), dof_per_box) for i in range(N)]
        for iBin, i in enumerate(_np.argsort(scaled_fitQty)):
            opstr = circuitList[i]
            fit, expected = scaled_fitQty[i], percentiles[iBin]
            if fit > expected:
                if opstr in circuitWeights: circuitWeights[opstr] *= expected / fit
                else: circuitWeights[opstr] = expected / fit

    return circuitWeights 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def ci_corr(self, sig=.05, upper_bound=None, lower_bound=None):
        """
        Returns the confidence intervals for the correlation coefficient

        Parameters
        ----------
        sig : float
            The significance level.  Default is .05

        upper_bound : float
            Maximum value the upper confidence limit can be.
            Default is  99% confidence limit assuming normality.

        lower_bound : float
            Minimum value the lower condidence limit can be.
            Default is 99% confidence limit assuming normality.

        Returns
        -------
        interval : tuple
            Confidence interval for the correlation

        """
        endog = self.endog
        nobs = self.nobs
        self.r0 = chi2.ppf(1 - sig, 1)
        point_est = np.corrcoef(endog[:, 0], endog[:, 1])[0, 1]
        if upper_bound is None:
            upper_bound = min(.999, point_est + \
                          2.5 * ((1. - point_est ** 2.) / \
                          (nobs - 2.)) ** .5)

        if lower_bound is None:
            lower_bound = max(- .999, point_est - \
                          2.5 * (np.sqrt((1. - point_est ** 2.) / \
                          (nobs - 2.))))

        llim = optimize.brenth(self._ci_limits_corr, lower_bound, point_est)
        ulim = optimize.brenth(self._ci_limits_corr, point_est, upper_bound)
        return llim, ulim 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def _fisher_confint(self, alpha: float = 0.05, observed: bool = False) -> List[float]:
        """Compute the `alpha` confidence interval based on the Fisher information.

        Args:
            alpha: The level of the confidence interval (must be <= 0.5), default to 0.05.
            observed: If True, use observed Fisher information.

        Returns:
            float: The alpha confidence interval based on the Fisher information
        Raises:
            AssertionError: Call run() first!
        """
        # Get the (observed) Fisher information
        fisher_information = None
        try:
            fisher_information = self._ret['fisher_information']
        except KeyError:
            raise AssertionError("Call run() first!")

        if observed:
            fisher_information = self._compute_fisher_information(observed=True)

        normal_quantile = norm.ppf(1 - alpha / 2)
        confint = np.real(self._ret['value']) + \
            normal_quantile / np.sqrt(fisher_information) * np.array([-1, 1])
        mapped_confint = [self.a_factory.value_to_estimation(bound) for bound in confint]
        return mapped_confint 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def _get_unsorted_edges():
    """P10 - P90 unsorted edge coordinates"""

    retval = {"low": chi2.ppf(0.1, 1), "high": chi2.ppf(0.9, 1)}

    return retval 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def plot_2d_GMMs(X, labels, means, covs, percentcontour=0.66, npoints=30):
    """
    Given an observation array, a label vector (integer values), and GMM mean
    and covariance parameters, plot the clusters and parameters.
    """

    clabels = set(labels)
    K = len(clabels)

    if len(means) != len(covs) != K:
        raise ValueError("Expecting the number of unique labels, means and"
                         "covariances to be the same!")

    phi = np.linspace(-np.pi, np.pi, npoints)

    circle = np.array([np.sin(phi), np.cos(phi)]).T

    figure(figsize=(10, 10))
    gca()

    colors = cm.hsv(np.arange(K)/float(K))
    for k, col in zip(clabels, colors):

        # points
        my_members = labels == k
        scatter(X[my_members, 0], X[my_members, 1], c=col, marker='o', s=20)

        # means
        cluster_center = means[k, :]
        scatter(cluster_center[0], cluster_center[1], c=col, marker='o', s=200)

        # covariance
        L = la.cholesky(np.array(covs[k]) * chi2.ppf(percentcontour, [3])
                        + 1e-5 * np.eye(covs[k].shape[0]))
        covpoints = circle.dot(L) + means[k, :]
        plot(covpoints[:, 0], covpoints[:, 1], color=col, linewidth=3)

    axis('tight')
    axis('equal')
    title('Clusters') 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def ljung_box_test(residuals, lags=[1,2,3], alpha=0.5):
    from statsmodels.stats.diagnostic import acorr_ljungbox
    from scipy.stats import chi2
    
    stat, pval = acorr_ljungbox(residuals, lags=lags)
    
    rows = []

    for ct, Q in enumerate(stat):
      lag = ct+1
      p_value = 1 - chi2.cdf(Q, df=lag)
      critical_value = chi2.ppf(1 - alpha, df=lag)
      rows.append([lag, Q, p_value, critical_value, 'H0 accepted' if Q > critical_value else 'H0 rejected'])
        
    return pd.DataFrame(rows, columns=['Lag','Statistic','p-Value','Critical Value', 'Result']) 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def ci_beta(self, param_num, beta_high, beta_low, sig=.05):
        """
        Returns the confidence interval for a regression
        parameter in the AFT model.

        Parameters
        ---------

        param_num: int
            Parameter number of interest

        beta_high: float
            Upper bound for the confidence interval

        beta_low:
            Lower bound for the confidence interval

        sig: float, optional
            Significance level.  Default is .05

        Notes
        ----
        If the function returns f(a) and f(b) must have different signs,
        consider widening the search area by adjusting beta_low and
        beta_high.

        Also note that this process is computational intensive.  There
        are 4 levels of optimization/solving.  From outer to inner:

        1) Solving so that llr-critical value = 0
        2) maximizing over nuisance parameters
        3) Using  EM at each value of nuisamce parameters
        4) Using the _modified_Newton optimizer at each iteration
           of the EM algorithm.

        Also, for very unlikely nuisance parameters, it is possible for
        the EM algorithm to not converge.  This is not an indicator
        that the solver did not find the correct solution.  It just means
        for a specific iteration of the nuisance parameters, the optimizer
        was unable to converge.

        If the user desires to verify the success of the optimization,
        it is recommended to test the limits using test_beta.

        """
        params = self.params()
        self.r0 = chi2.ppf(1 - sig, 1)
        ll = optimize.brentq(self._ci_limits_beta, beta_low,
                             params[param_num], (param_num))
        ul = optimize.brentq(self._ci_limits_beta,
                             params[param_num], beta_high, (param_num))
        return ll, ul 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def conf_int_el(self, param_num, upper_bound=None,
                       lower_bound=None, sig=.05, method='nm',
                       stochastic_exog=1):
        """
        Returns the confidence interval for a regression parameter when the
        regression is forced through the origin

        Parameters
        ----------
        param_num : int
            The parameter number to be tested.  Note this uses python
            indexing but the '0' parameter refers to the intercept term

        upper_bound : float
            The maximum value the upper confidence limit can be.  The
            closer this is to the confidence limit, the quicker the
            computation.  Default is .00001 confidence limit under normality

        lower_bound : float
            The minimum value the lower confidence limit can be.
            Default is .00001 confidence limit under normality

        sig : float, optional
            The significance level.  Default .05

        method : str, optional
             Algorithm to optimize of nuisance params.  Can be 'nm' or
            'powell'.  Default is 'nm'.

        Returns
        -------
        ci: tuple
            The confidence interval for the parameter 'param_num'
        """
        r0 = chi2.ppf(1 - sig, 1)
        param_num = np.array([param_num])
        if upper_bound is None:
            upper_bound = (np.squeeze(self.model.fit().
                                      conf_int(.0001)[param_num])[1])
        if lower_bound is None:
            lower_bound = (np.squeeze(self.model.fit().conf_int(.00001)
                                      [param_num])[0])
        f = lambda b0:  self.el_test(np.array([b0]), param_num,
                                     method=method,
                                 stochastic_exog=stochastic_exog)[0] - r0
        lowerl = optimize.brentq(f, lower_bound, self.params[param_num])
        upperl = optimize.brentq(f, self.params[param_num], upper_bound)
        return (lowerl, upperl) 

# 需要導入模塊: from scipy.stats import chi2 [as 別名]
# 或者: from scipy.stats.chi2 import ppf [as 別名]
def ci_var(self, lower_bound=None, upper_bound=None, sig=.05):
        """
        Returns the confidence interval for the variance.

        Parameters
        ----------
        lower_bound : float
            The minimum value the lower confidence interval can
            take. The p-value from test_var(lower_bound) must be lower
            than 1 - significance level. Default is .99 confidence
            limit assuming normality

        upper_bound : float
            The maximum value the upper confidence interval
            can take. The p-value from test_var(upper_bound) must be lower
            than 1 - significance level.  Default is .99 confidence
            limit assuming normality

        sig : float
            The significance level. Default is .05

        Returns
        --------
        Interval : tuple
            Confidence interval for the variance

        Examples
        --------
        >>> import numpy as np
        >>> import statsmodels.api as sm
        >>> random_numbers = np.random.standard_normal(100)
        >>> el_analysis = sm.emplike.DescStat(random_numbers)
        >>> el_analysis.ci_var()
        (0.7539322567470305, 1.229998852496268)
        >>> el_analysis.ci_var(.5, 2)
        (0.7539322567469926, 1.2299988524962664)

        Notes
        -----
        If the function returns the error f(a) and f(b) must have
        different signs, consider lowering lower_bound and raising
        upper_bound.
        """
        endog = self.endog
        if upper_bound is None:
            upper_bound = ((self.nobs - 1) * endog.var()) / \
              (chi2.ppf(.0001, self.nobs - 1))
        if lower_bound is None:
            lower_bound = ((self.nobs - 1) * endog.var()) / \
              (chi2.ppf(.9999, self.nobs - 1))
        self.r0 = chi2.ppf(1 - sig, 1)
        llim = optimize.brentq(self._ci_limits_var, lower_bound, endog.var())
        ulim = optimize.brentq(self._ci_limits_var, endog.var(), upper_bound)
        return llim, ulim