code: def d2logpdf_dlink2(self, inv_link_f, y, Y_metadata=None):
          
          e = y - inv_link_f
          hess = ((self.v + 1)*(e**2 - self.v*self.sigma2)) / ((self.sigma2*self.v + e**2)**2)
          return hess
docs: Hessian at y, given link(f), w.r.t link(f)
          i.e. second derivative logpdf at y given link(f_i) and link(f_j)  w.r.t link(f_i) and link(f_j)
          The hessian will be 0 unless i == j
  
          .. math::
              \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = \\frac{(v+1)((y_{i}-\lambda(f_{i}))^{2} - \\sigma^{2}v)}{((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: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f)
          :rtype: Nx1 array
  
          .. Note::
              Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
              (the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))