code: def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None):
          
          s_4 = 1.0/(self.variance**2)
          dlik_grad_dsigma = -s_4*y + s_4*link_f
          return dlik_grad_dsigma
docs: 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