def d2logpdf_df2(self, f, y, Y_metadata=None):
        """
        Evaluates the link function link(f) then computes the second derivative of log likelihood using it
        Uses the Faa di Bruno's formula for the chain rule

        .. math::
            \\frac{d^{2}\\log p(y|\\lambda(f))}{df^{2}} = \\frac{d^{2}\\log p(y|\\lambda(f))}{d^{2}\\lambda(f)}\\left(\\frac{d\\lambda(f)}{df}\\right)^{2} + \\frac{d\\log p(y|\\lambda(f))}{d\\lambda(f)}\\frac{d^{2}\\lambda(f)}{df^{2}}

        :param f: latent variables f
        :type f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata which is not used in student t distribution - not used
        :returns: second derivative of log likelihood evaluated for this point (diagonal only)
        :rtype: 1xN array
        """
        if isinstance(self.gp_link, link_functions.Identity):
            d2logpdf_df2 = self.d2logpdf_dlink2(f, y, Y_metadata=Y_metadata)
        else:
            inv_link_f = self.gp_link.transf(f)
            d2logpdf_dlink2 = self.d2logpdf_dlink2(inv_link_f, y, Y_metadata=Y_metadata)
            dlink_df = self.gp_link.dtransf_df(f)
            dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata)
            d2link_df2 = self.gp_link.d2transf_df2(f)
            d2logpdf_df2 = chain_2(d2logpdf_dlink2, dlink_df, dlogpdf_dlink, d2link_df2)
        return d2logpdf_df2