def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None):
s_4 = <NUM_LIT:1.0>/(self.variance**<NUM_LIT:2>)<EOL>dlik_grad_dsigma = -s_4*y + s_4*link_f<EOL>return dlik_grad_dsigma<EOL>
Derivative of the dlogpdf_dlink w.r.t variance parameter (noise_variance)

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

: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 likelihood evaluated at points link(f) w.r.t variance parameter
:rtype: Nx1 array