Log Likelihood Function given link(f)

        .. math::
            \\ln p(y_{i}|\lambda(f_{i})) = \\alpha_{i}\\log \\beta - \\log \\Gamma(\\alpha_{i}) + (\\alpha_{i} - 1)\\log y_{i} - \\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 logpdf_link(self, link_f, y, Y_metadata=None):
        """
        Log Likelihood Function given link(f)

        .. math::
            \\ln p(y_{i}|\lambda(f_{i})) = \\alpha_{i}\\log \\beta - \\log \\Gamma(\\alpha_{i}) + (\\alpha_{i} - 1)\\log y_{i} - \\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

        """
        #alpha = self.gp_link.transf(gp)*self.beta
        #return (1. - alpha)*np.log(obs) + self.beta*obs - alpha * np.log(self.beta) + np.log(special.gamma(alpha))
        alpha = link_f*self.beta
        log_objective = alpha*np.log(self.beta) - np.log(special.gamma(alpha)) + (alpha - 1)*np.log(y) - self.beta*y
        return log_objective