def d2logpdf_dlink2_dvar(self, link_f, y, Y_metadata=None):
s_4 = <NUM_LIT:1.0>/(self.variance**<NUM_LIT:2>)<EOL>N = y.shape[<NUM_LIT:0>]<EOL>D = link_f.shape[<NUM_LIT:1>]<EOL>d2logpdf_dlink2_dvar = np.ones((N, D))*s_4<EOL>return d2logpdf_dlink2_dvar<EOL>
Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (noise_variance)

.. math::
    \\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)}) = \\frac{1}{\\sigma^{4}}

: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: derivative of log hessian evaluated at points link(f_i) and link(f_j) w.r.t variance parameter
:rtype: Nx1 array