def _upper_confidence_bound(mu, sigma, kappa=2.):
    """
    Calculates the upper confidence bound at the point 'x', for which:
        mu = mean(x)
        sigma = std(x)

    Parameters
    ----------
    mu : array_like, shape (n,)
        Mean.
    sigma : array_like, shape (n,)
        Standard deviation.
    kappa : float
        Exploration parameter.

    Returns
    -------
    ei : array_like, shape (n,)
        Expected improvement at point 'x'.
    """

    return mu + kappa * sigma