def Ey(self, f):
        r"""
        Expected value of the Poisson likelihood.

        Parameters
        ----------
        f: ndarray
            latent function from the GLM prior (:math:`\mathbf{f} =
            \boldsymbol\Phi \mathbf{w}`)

        Returns
        -------
        Ey: ndarray
            expected value of y, :math:`\mathbb{E}[\mathbf{y}|\mathbf{f}]`.
        """
        return np.exp(f) if self.tranfcn == 'exp' else softplus(f)
r"""
        Expected value of the Poisson likelihood.

        Parameters
        ----------
        f: ndarray
            latent function from the GLM prior (:math:`\mathbf{f} =
            \boldsymbol\Phi \mathbf{w}`)

        Returns
        -------
        Ey: ndarray
            expected value of y, :math:`\mathbb{E}[\mathbf{y}|\mathbf{f}]`.