brsa.py 文件源码

def prior_GP_var_half_cauchy(y_invK_y, n_y, tau_range):
    """ Imposing a half-Cauchy prior onto the standard deviation (tau)
        of the Gaussian Process which is in turn a prior imposed over
        a function y = f(x).
        The scale parameter of the half-Cauchy prior is tau_range.
        The function returns the MAP estimate of tau^2 and
        log(p(tau|tau_range)) for the MAP value of tau^2,
        where tau_range describes the reasonable range of tau
        in the half-Cauchy prior.
        An alternative form of prior is inverse-Gamma prior on tau^2.
        Inverse-Gamma prior penalizes for both very small and very
        large values of tau, while half-Cauchy prior only penalizes
        for very large values of tau.
        For more information on usage, see description in BRSA class:
        `.BRSA`
    """
    tau2 = (y_invK_y - n_y * tau_range**2
            + np.sqrt(n_y**2 * tau_range**4 + (2 * n_y + 8)
                      * tau_range**2 * y_invK_y + y_invK_y**2))\
        / 2 / (n_y + 2)
    log_ptau = scipy.stats.halfcauchy.logpdf(
        tau2**0.5, scale=tau_range)
    return tau2, log_ptau