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

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

        :param inv_link_f: latent variables inv_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: Nx1 array
        """
        e = y - inv_link_f
        dlogpdf_dlink_dvar = (self.v*(self.v+1)*(-e))/((self.sigma2*self.v + e**2)**2)
        return dlogpdf_dlink_dvar