def dlogpdf_link_dvar(self, inv_link_f, y, Y_metadata=None):
e = y - inv_link_f<EOL>e2 = np.square(e)<EOL>dlogpdf_dvar = self.v*(e2 - self.sigma2)/(<NUM_LIT:2>*self.sigma2*(self.sigma2*self.v + e2))<EOL>return dlogpdf_dvar<EOL>
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