def dlogpdf_link_dvar(self, inv_link_f, y, Y_metadata=None):
        """
        Gradient of the log-likelihood function at y given f, w.r.t variance parameter (t_noise)

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

        :param inv_link_f: latent variables link(f)
        :type inv_link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata which is not used in student t distribution
        :returns: derivative of likelihood evaluated at points f w.r.t variance parameter
        :rtype: float
        """
        e = y - inv_link_f
        e2 = np.square(e)
        dlogpdf_dvar = self.v*(e2 - self.sigma2)/(2*self.sigma2*(self.sigma2*self.v + e2))
        return dlogpdf_dvar