def dlogpdf_link_dvar(self, link_f, y, Y_metadata=None):
e = y - link_f<EOL>s_4 = <NUM_LIT:1.0>/(self.variance**<NUM_LIT:2>)<EOL>dlik_dsigma = -<NUM_LIT:0.5>/self.variance + <NUM_LIT:0.5>*s_4*np.square(e)<EOL>return dlik_dsigma<EOL>
Gradient of the log-likelihood function at y given link(f), w.r.t variance parameter (noise_variance)

.. math::
    \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\sigma^{2}} = -\\frac{N}{2\\sigma^{2}} + \\frac{(y_{i} - \\lambda(f_{i}))^{2}}{2\\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 likelihood evaluated at points link(f) w.r.t variance parameter
:rtype: float