def d2logpdf_dlink2_dvar(self, inv_link_f, y, Y_metadata=None):
e = y - inv_link_f<EOL>d2logpdf_dlink2_dvar = ( (self.v*(self.v+<NUM_LIT:1>)*(self.sigma2*self.v - <NUM_LIT:3>*(e**<NUM_LIT:2>)))<EOL>/ ((self.sigma2*self.v + (e**<NUM_LIT:2>))**<NUM_LIT:3>)<EOL>)<EOL>return d2logpdf_dlink2_dvar<EOL>
Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (t_noise)

.. math::
    \\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}f}) = \\frac{v(v+1)(\\sigma^{2}v - 3(y_{i} - \lambda(f_{i}))^{2})}{(\\sigma^{2}v + (y_{i} - \lambda(f_{i}))^{2})^{3}}

: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 hessian evaluated at points f and f_j w.r.t variance parameter
:rtype: Nx1 array