def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
N = y.shape[<NUM_LIT:0>]<EOL>D = link_f.shape[<NUM_LIT:1>]<EOL>hess = -(<NUM_LIT:1.0>/self.variance)*np.ones((N, D))<EOL>return hess<EOL>
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))