def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
        """
        Hessian at y, given link(f), w.r.t link(f)
        i.e. second derivative logpdf at y given link(f_i) and link(f_j)  w.r.t link(f_i) and link(f_j)
        The hessian will be 0 unless i == j

        .. math::
            \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = -\\beta^{2}\\frac{d\\Psi(\\alpha_{i})}{d\\alpha_{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 gamma distribution
        :returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f)
        :rtype: Nx1 array

        .. Note::
            Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
            (the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
        """
        hess = -special.polygamma(1, self.beta*link_f)*(self.beta**2)
        #old
        #return -self.gp_link.d2transf_df2(gp)*self.beta*np.log(obs) + special.polygamma(1,self.gp_link.transf(gp)*self.beta)*(self.gp_link.dtransf_df(gp)*self.beta)**2 + special.psi(self.gp_link.transf(gp)*self.beta)*self.gp_link.d2transf_df2(gp)*self.beta
        return hess
def d2logpdf_dlink2 ( self , link_f , y , Y_metadata = None ) : hess = - special . polygamma ( 1 , self . beta * link_f ) * ( self . beta ** 2 ) return hess
Hessian at y, given link(f), w.r.t link(f)
        i.e. second derivative logpdf at y given link(f_i) and link(f_j)  w.r.t link(f_i) and link(f_j)
        The hessian will be 0 unless i == j

        .. math::
            \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = -\\beta^{2}\\frac{d\\Psi(\\alpha_{i})}{d\\alpha_{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 gamma distribution
        :returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f)
        :rtype: Nx1 array

        .. Note::
            Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
            (the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))