def METHOD_NAME(values, samples):
    """Add Gaussian noise to each bootstrap replicate.
    The result is used to compute a "smoothed bootstrap," where the added noise
    ensures that for small samples (e.g. number of bins in the segment) the
    bootstrapped CI is close to the standard error of the mean, as it should be.
    Conceptually, sample from a KDE instead of the values themselves.
    This addresses the issue that small segments (#bins < #replicates) don't
    fully represent the underlying distribution, in particular the extreme
    values, so the CI is too narrow. For single-bin segments in particular,
    the confidence interval will always have zero width unless the samples are
    smoothed.
    Standard deviation of the noise added to each bin comes from each bin's
    weight, which is an estimate of (1-variance).
    Parameters
    ----------
    values : np.ndarray
        Original log2 values within the segment.
    samples : list of np.ndarray
        Bootstrap replicates as (value_sample, weight_sample).
    Returns
    -------
    `samples` with random N(0, pop_sd) added to each value, and
    weights unchanged.
    """
    k = len(values)
    # KDE bandwidth narrows for larger sample sizes
    # Following Silverman's Rule and Polansky 1995,
    # but requiring k=1 -> bw=1 for consistency
    bw = k ** (-1 / 4)
    samples = [(v + (bw * np.sqrt(1 - w) * np.random.randn(k)), w) for v, w in samples]
    return samples