Module « scipy.stats »

Fonction bayes_mvs - module scipy.stats

Signature de la fonction bayes_mvs

def bayes_mvs(data, alpha=0.9) 

Description

bayes_mvs.__doc__

    Bayesian confidence intervals for the mean, var, and std.

    Parameters
    ----------
    data : array_like
        Input data, if multi-dimensional it is flattened to 1-D by `bayes_mvs`.
        Requires 2 or more data points.
    alpha : float, optional
        Probability that the returned confidence interval contains
        the true parameter.

    Returns
    -------
    mean_cntr, var_cntr, std_cntr : tuple
        The three results are for the mean, variance and standard deviation,
        respectively.  Each result is a tuple of the form::

            (center, (lower, upper))

        with `center` the mean of the conditional pdf of the value given the
        data, and `(lower, upper)` a confidence interval, centered on the
        median, containing the estimate to a probability ``alpha``.

    See Also
    --------
    mvsdist

    Notes
    -----
    Each tuple of mean, variance, and standard deviation estimates represent
    the (center, (lower, upper)) with center the mean of the conditional pdf
    of the value given the data and (lower, upper) is a confidence interval
    centered on the median, containing the estimate to a probability
    ``alpha``.

    Converts data to 1-D and assumes all data has the same mean and variance.
    Uses Jeffrey's prior for variance and std.

    Equivalent to ``tuple((x.mean(), x.interval(alpha)) for x in mvsdist(dat))``

    References
    ----------
    T.E. Oliphant, "A Bayesian perspective on estimating mean, variance, and
    standard-deviation from data", https://scholarsarchive.byu.edu/facpub/278,
    2006.

    Examples
    --------
    First a basic example to demonstrate the outputs:

    >>> from scipy import stats
    >>> data = [6, 9, 12, 7, 8, 8, 13]
    >>> mean, var, std = stats.bayes_mvs(data)
    >>> mean
    Mean(statistic=9.0, minmax=(7.103650222612533, 10.896349777387467))
    >>> var
    Variance(statistic=10.0, minmax=(3.176724206..., 24.45910382...))
    >>> std
    Std_dev(statistic=2.9724954732045084, minmax=(1.7823367265645143, 4.945614605014631))

    Now we generate some normally distributed random data, and get estimates of
    mean and standard deviation with 95% confidence intervals for those
    estimates:

    >>> n_samples = 100000
    >>> data = stats.norm.rvs(size=n_samples)
    >>> res_mean, res_var, res_std = stats.bayes_mvs(data, alpha=0.95)

    >>> import matplotlib.pyplot as plt
    >>> fig = plt.figure()
    >>> ax = fig.add_subplot(111)
    >>> ax.hist(data, bins=100, density=True, label='Histogram of data')
    >>> ax.vlines(res_mean.statistic, 0, 0.5, colors='r', label='Estimated mean')
    >>> ax.axvspan(res_mean.minmax[0],res_mean.minmax[1], facecolor='r',
    ...            alpha=0.2, label=r'Estimated mean (95% limits)')
    >>> ax.vlines(res_std.statistic, 0, 0.5, colors='g', label='Estimated scale')
    >>> ax.axvspan(res_std.minmax[0],res_std.minmax[1], facecolor='g', alpha=0.2,
    ...            label=r'Estimated scale (95% limits)')

    >>> ax.legend(fontsize=10)
    >>> ax.set_xlim([-4, 4])
    >>> ax.set_ylim([0, 0.5])
    >>> plt.show()