Derivative of the dlogpdf_dlink w.r.t variance parameter (noise_variance)

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

        :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 likelihood evaluated at points link(f) w.r.t variance parameter
        :rtype: Nx1 array

def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None):
        """
        Derivative of the dlogpdf_dlink w.r.t variance parameter (noise_variance)

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

        :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 likelihood evaluated at points link(f) w.r.t variance parameter
        :rtype: Nx1 array
        """
        s_4 = 1.0/(self.variance**2)
        dlik_grad_dsigma = -s_4*y + s_4*link_f
        return dlik_grad_dsigma