code: def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
          
          N = y.shape[0]
          D = link_f.shape[1]
          hess = -(1.0/self.variance)*np.ones((N, D))
          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) 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}f} = -\\frac{1}{\\sigma^{2}}
  
          :param link_f: latent variables link(f)
          :type link_f: Nx1 array
          :param y: data
          :type y: Nx1 array
          :param Y_metadata: Y_metadata not used in gaussian
          :returns: Diagonal of log hessian matrix (second derivative of log likelihood evaluated at points link(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))