Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (noise_variance)

        .. math::
            \\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)}) = \\frac{1}{\\sigma^{4}}

        :param link_f: latent variables link(f)
        :type link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: derivative of log hessian evaluated at points link(f_i) and link(f_j) w.r.t variance parameter
        :rtype: Nx1 array

def d2logpdf_dlink2_dvar(self, link_f, y, Y_metadata=None):
        """
        Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (noise_variance)

        .. math::
            \\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)}) = \\frac{1}{\\sigma^{4}}

        :param link_f: latent variables link(f)
        :type link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: derivative of log hessian evaluated at points link(f_i) and link(f_j) w.r.t variance parameter
        :rtype: Nx1 array
        """
        s_4 = 1.0/(self.variance**2)
        N = y.shape[0]
        D = link_f.shape[1]
        d2logpdf_dlink2_dvar = np.ones((N, D))*s_4
        return d2logpdf_dlink2_dvar