def pdf_link(self, link_f, y, Y_metadata=None):
        """
        Likelihood function given link(f)

        .. math::
            \\ln p(y_{i}|\\lambda(f_{i})) = -\\frac{N \\ln 2\\pi}{2} - \\frac{\\ln |K|}{2} - \\frac{(y_{i} - \\lambda(f_{i}))^{T}\\sigma^{-2}(y_{i} - \\lambda(f_{i}))}{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: likelihood evaluated for this point
        :rtype: float
        """
        #Assumes no covariance, exp, sum, log for numerical stability
        return np.exp(np.sum(np.log(stats.norm.pdf(y, link_f, np.sqrt(self.variance)))))