code: def d2logpdf_dlink2_dvar(self, inv_link_f, y, Y_metadata=None):
          
          e = y - inv_link_f
          d2logpdf_dlink2_dvar = ( (self.v*(self.v+1)*(self.sigma2*self.v - 3*(e**2)))
                                / ((self.sigma2*self.v + (e**2))**3)
                             )
          return d2logpdf_dlink2_dvar
docs: 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