Likelihood function given link(f)

        .. math::
            p(y_{i}|\\lambda(f_{i})) = \\frac{\\beta^{\\alpha_{i}}}{\\Gamma(\\alpha_{i})}y_{i}^{\\alpha_{i}-1}e^{-\\beta y_{i}}\\\\
            \\alpha_{i} = \\beta y_{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 which is not used in poisson distribution
        :returns: likelihood evaluated for this point
        :rtype: float

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

        .. math::
            p(y_{i}|\\lambda(f_{i})) = \\frac{\\beta^{\\alpha_{i}}}{\\Gamma(\\alpha_{i})}y_{i}^{\\alpha_{i}-1}e^{-\\beta y_{i}}\\\\
            \\alpha_{i} = \\beta y_{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 which is not used in poisson distribution
        :returns: likelihood evaluated for this point
        :rtype: float
        """
        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
        #return stats.gamma.pdf(obs,a = self.gp_link.transf(gp)/self.variance,scale=self.variance)
        alpha = link_f*self.beta
        objective = (y**(alpha - 1.) * np.exp(-self.beta*y) * self.beta**alpha)/ special.gamma(alpha)
        return np.exp(np.sum(np.log(objective)))